fact stringlengths 9 20.3k | type stringclasses 2 values | library stringclasses 116 values | imports listlengths 0 239 | filename stringlengths 21 103 | symbolic_name stringlengths 1 92 | docstring null |
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depends_on_def = depends_on alist x y <=> RTC (\a b. ?deps. ALOOKUP alist a = SOME deps /\ MEM b deps /\ MEM b (MAP FST alist)) x y | definition | examples/algorithms | [] | examples/algorithms/topological_sortScript.sml | depends_on_def | null |
depends_on1_def = depends_on1 alist a b = ∃deps. ALOOKUP alist a = SOME deps ∧ MEM b deps ∧ MEM b (MAP FST alist) | definition | examples/algorithms | [] | examples/algorithms/topological_sortScript.sml | depends_on1_def | null |
TC_depends_on_def = TC_depends_on alist ⇔ TC $ depends_on1 alist | definition | examples/algorithms | [] | examples/algorithms/topological_sortScript.sml | TC_depends_on_def | null |
TC_depends_on_weak_def = TC_depends_on_weak alist ⇔ TC (λa b. ∃deps. ALOOKUP alist a = SOME deps ∧ MEM b deps) | definition | examples/algorithms | [] | examples/algorithms/topological_sortScript.sml | TC_depends_on_weak_def | null |
map_eq_id : (∀a. a ∈ setAF x ⇒ f a = a) ∧ (∀b. b ∈ setBF x ⇒ g b = b) ⇒ mapF f g x = x | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | map_eq_id | null |
IN_UNCURRY : (x,y) ∈ UNCURRY R ⇔ R x y | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | IN_UNCURRY | null |
relO_EQ : relF R1 R2 O relF S1 S2 = relF (R1 O S1) (R2 O S2) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | relO_EQ | null |
alg_nonempty : alg(A, s : (β,α)F -> α) ⇒ A ≠ ∅ | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | alg_nonempty | null |
minset_is_alg : alg (minset s, s) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | minset_is_alg | null |
IN_minset : x IN minset s ⇔ ∀A. alg(A,s) ⇒ x IN A | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | IN_minset | null |
homs_on_same_domain : hom h (A,s) (B,t) ∧ (∀a. a ∈ A ⇒ h' a = h a) ⇒ hom h' (A,s) (B,t) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | homs_on_same_domain | null |
homs_compose : hom f (A : α set,s : (δ,α)F -> α) (B : β set,t) ∧ hom g (B,t) (C : γ set,u) ⇒ hom (g o f) (A,s) (C,u) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | homs_compose | null |
minset_ind : ∀P. (∀x. setBF x ⊆ minset s ∧ (∀y. y ∈ setBF x ⇒ P y) ⇒ P (s x)) ⇒ ∀x. x ∈ minset s ⇒ P x | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | minset_ind | null |
minsub_gives_unique_homs : hom h1 (minset s, s) (C,t) ∧ hom h2 (minset s,s) (C,t) ⇒ ∀a. a ∈ minset s ⇒ h1 a = h2 a | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | minsub_gives_unique_homs | null |
subalgs_preserve_homs : subalg A1 A2 ∧ hom f A2 C ⇒ hom f A1 C | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | subalgs_preserve_homs | null |
minsub_subalg : alg(A,s) ⇒ subalg (minset s, s) (A,s) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | minsub_subalg | null |
minsub_I_subalg : alg(A,s) ⇒ hom I (minset s, s) (A,s) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | minsub_I_subalg | null |
bigprod_isalg : alg bigprod | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | bigprod_isalg | null |
bigprod_proj : alg (A,s) ⇒ hom (λf. f (mkIx (A,s))) bigprod (A,s) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | bigprod_proj | null |
minbigprod_has_unique_homs : let s = SND (bigprod : ((α,β)idx -> α, β) alg) in ∀A f. alg ((A, f) : (α,β) alg) ⇒ ∃!h. (∀d. d ∉ minset s ⇒ h d = ARB) ∧ hom h (minset s, s) (A, f) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | minbigprod_has_unique_homs | null |
minset_unique_homs : hom h1 (minset s, s) (B,t) ∧ hom h2 (minset s, s) (B,t) ⇒ ∀a. a ∈ minset s ⇒ h1 a = h2 a | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | minset_unique_homs | null |
KK_mono : ∀β α. α < β ⇒ KK s α ⊆ KK s β | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | KK_mono | null |
KK_mono_LE : ∀α β. α ≤ β ⇒ KK s α ⊆ KK s β | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | KK_mono_LE | null |
KK_SUB_min : ∀α. KK s α ⊆ minset s | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | KK_SUB_min | null |
KK_fixp_is_alg : { s x | x | setBF x ⊆ KK s ε } = KK s ε ⇒ alg(KK s ε, s) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | KK_fixp_is_alg | null |
KK_sup : ords ≼ 𝕌(:num + 'a) ⇒ KK s (sup ords : 'a ordinal) = BIGUNION (IMAGE (KK s) ords) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | KK_sup | null |
KK_preds_subset : BIGUNION (IMAGE (KK s) (preds α)) ⊆ KK s α | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | KK_preds_subset | null |
KK_thm : KK s α = if α = 0 then ∅ else BIGUNION (IMAGE (λa. { s fv | fv | setBF fv ⊆ KK s a}) (preds α)) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | KK_thm | null |
sucbnd_suffices : ω ≤ (bd : γ ordinal) ∧ (∀x : (α,β)F. setBF x ≼ preds bd) ⇒ alg (KK (s:(α,β)F -> β) (csuc bd), s) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | sucbnd_suffices | null |
KKbnd_EQ_minset : ω ≤ (bd : γ ordinal) ∧ (∀x : (α,β)F. setBF x ≼ preds bd) ⇒ KK (s : (α,β)F -> β) (csuc bd) = minset s | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | KKbnd_EQ_minset | null |
nontrivialBs : (∃x:(α,β)F. setBF x ≠ ∅) ⇒ ∀B. (B:β set) ≼ Fin 𝕌(:α) B | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | nontrivialBs | null |
CBDb : ω ≤ (bd : γ ordinal) ∧ (∀x:(α,β)F. setBF x ≼ preds bd) ∧ (∃x:(α,γ ordinal)F. setBF x ≠ ∅) ⇒ ∀B:β set. 𝟚 ≼ B ⇒ Fin 𝕌(:α) B ≼ B ** cardSUC (Fin 𝕌(:α) (preds bd)) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | CBDb | null |
preds_bd_lemma : setBF (gv : (α,γ ordinal)F) ≠ ∅ ⇒ preds (bd:γ ordinal) ≼ preds (oleast a:(α,γ ordinal)F ordinal. preds a ≈ Fin 𝕌(:α) (preds bd)) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | preds_bd_lemma | null |
preds_csuc_lemma : preds a ≼ preds (csuc a) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | preds_csuc_lemma | null |
Fin_MONO : s ⊆ t ⇒ Fin A s ⊆ Fin A t | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | Fin_MONO | null |
Fin_cardleq : s ≼ t ⇒ Fin A s ≼ Fin A t | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | Fin_cardleq | null |
cardADD2 : s ≼ s +_c 𝟚 | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | cardADD2 | null |
alg_cardinality_bound : ω ≤ (bd : γ ordinal) ∧ (∀x:(α,β+bool)F. setBF x ≼ preds bd) ∧ (∃x:(α,γ ordinal)F. setBF x ≠ ∅) ⇒ KK (s:(α,β)F -> β) (csuc bd) ≼ 𝟚 ** (cardSUC $ Fin 𝕌(:α) (preds bd)) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | alg_cardinality_bound | null |
copy_alg_back : (A:α set) ≼ (B:β set) ∧ alg (A, s : (γ,α)F -> α) ⇒ ∃(B0:β set) s' h j. hom h (B0,s') (A,s) ∧ hom j (A,s) (B0,s') ∧ (∀a. a ∈ A ⇒ h (j a) = a) ∧ (∀b. b ∈ B0 ⇒ j (h b) = b) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | copy_alg_back | null |
IAlg_isalg : alg (IAlg, Cons) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | IAlg_isalg | null |
hom_arbification : hom h (A,s) (B,t) ⇒ ∃j. hom j (A,s) (B,t) ∧ ∀x. x ∉ A ⇒ j x = ARB | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | hom_arbification | null |
initiality0 : ∀(t:(α,γ)F -> γ) (G:γ set). alg(G,t) ⇒ ∃!h. hom h (IAlg,Cons) (G,t) ∧ ∀x. x ∉ IAlg ⇒ h x = ARB | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | initiality0 | null |
inhabited : ∃w. IAlg w | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | inhabited | null |
alg_Fin : alg (A,s) ⇒ alg (Fin 𝕌(:β) A, mapF I s) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | alg_Fin | null |
hom_arbify : hom (arbify A f) (A,s : (γ,α)F -> α) (B,t : (γ,β)F -> β) ⇔ hom f (A,s) (B,t) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | hom_arbify | null |
iso0 : BIJ Cons (Fin 𝕌(:α) IAlg) IAlg | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | iso0 | null |
NCONS_isalg : alg (UNIV, NCONS) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | NCONS_isalg | null |
hom_nty_ABS : hom nty_ABS (IAlg,Cons) (UNIV,NCONS) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | hom_nty_ABS | null |
hom_nty_REP : hom nty_REP (UNIV, NCONS) (IAlg, Cons) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | hom_nty_REP | null |
initiality_hom : alg(B,t) ⇒ ∃!h. hom h (UNIV,NCONS) (B,t) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | initiality_hom | null |
UNIQUE_SKOLEM : (∀x. ∃!y. P x y) ⇔ ∃!f. ∀x. P x (f x) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | UNIQUE_SKOLEM | null |
minset_Cons : minset Cons = IAlg | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | minset_Cons | null |
ALL_Ialg : (∀ia. ia ∈ IAlg ⇒ P ia) ⇔ (∀n. P (nty_REP n)) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | ALL_Ialg | null |
ALL_Ialgv : (∀av. setBF av ⊆ IAlg ⇒ P av) ⇔ (∀n. P (mapF I nty_REP n)) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | ALL_Ialgv | null |
IN_setBF : (∀y. y ∈ setBF x ⇒ Q (nty_ABS y)) ⇔ x ∈ Fin 𝕌(:α) (Q o nty_ABS) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | IN_setBF | null |
Cons_NCONS : setBF x ⊆ IAlg ⇒ Cons x = nty_REP (NCONS (mapF I nty_ABS x)) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | Cons_NCONS | null |
abs_o_rep : nty_ABS o nty_REP = I | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | abs_o_rep | null |
setBF_applied : setBF x v ⇔ v ∈ setBF x | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | setBF_applied | null |
NCONS_comp : NCONS = nty_ABS o Cons o mapF I nty_REP | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | NCONS_comp | null |
iso : BIJ NCONS (Fin 𝕌(:α) 𝕌(:α nty)) 𝕌(:α nty) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | iso | null |
Fin_UNIV : Fin UNIV UNIV = UNIV | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | Fin_UNIV | null |
NCONS_11 : NCONS x = NCONS y ⇔ x = y | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | NCONS_11 | null |
MAP_ID : ∀n. MAP I n = n | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | MAP_ID | null |
MAP_COMPOSE : ∀n. MAP f (MAP g n) = MAP (f o g) n | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | MAP_COMPOSE | null |
SET_MAP : ∀n. SET (MAP f n) = IMAGE f (SET n) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | SET_MAP | null |
MAP_CONG : ∀n. (∀a. a ∈ SET n ⇒ f a = g a) ⇒ MAP f n = MAP g n | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | MAP_CONG | null |
Fin_def = Fin As Bs = { a : (α,β) F | setAF a ⊆ As ∧ setBF a ⊆ Bs } | definition | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | Fin_def | null |
relF_def = relF R1 R2 x y ⇔ ∃z. setAF z ⊆ UNCURRY R1 ∧ setBF z ⊆ UNCURRY R2 ∧ mapF FST FST z = x ∧ mapF SND SND z = y | definition | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | relF_def | null |
alg_def = alg (A : α set, s : (β,α) F -> α) ⇔ ∀x. x ∈ Fin UNIV A ⇒ s x ∈ A | definition | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | alg_def | null |
minset_def = minset (s : (β,α)F -> α) = BIGINTER { B | alg(B,s) } | definition | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | minset_def | null |
hom_def = hom h (A,s) (B,t) ⇔ alg(A,s) ∧ alg(B,t) ∧ (∀a. a IN A ⇒ h a IN B) ∧ ∀af. af ∈ Fin UNIV A ⇒ t (mapF I h af) = h (s af) | definition | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | hom_def | null |
subalg_def = subalg (A,s) (B,t) ⇔ alg(A,s) ∧ alg (B,t) ∧ (∀af. af ∈ Fin UNIV A ⇒ s af = t af) ∧ A ⊆ B | definition | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | subalg_def | null |
bigprod_def = bigprod : ((α,β)idx -> α, β) alg = ({ f | ∀i. f i ∈ FST (dIx i) }, λfv i. SND (dIx i) $ mapF I (λf. f i) fv) | definition | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | bigprod_def | null |
IAlg_def = IAlg = minset (SND $ bigprod : ('a algty, 'a) alg) | definition | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | IAlg_def | null |
Cons_def = Cons = SND $ bigprod : ('a algty,'a)alg | definition | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | Cons_def | null |
arbify_def = arbify A f x = if x ∈ A then f x else ARB | definition | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | arbify_def | null |
NCONS_def = NCONS (x : (α, α nty)F) = nty_ABS $ Cons $ mapF I nty_REP x | definition | examples/bnf-datatypes | [] | examples/bnf-datatypes/bnfAlgebraScript.sml | NCONS_def | null |
sumsetA_EQ_EMPTY : sumsetA s = {} ⇔ ∃x. s = INR x | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | sumsetA_EQ_EMPTY | null |
sumsetB_EQ_EMPTY : sumsetB s = {} ⇔ ∃x. s = INL x | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | sumsetB_EQ_EMPTY | null |
sumsetA_SUM_MAP : sumsetA (SUM_MAP f g s) = IMAGE f (sumsetA s) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | sumsetA_SUM_MAP | null |
sumsetB_SUM_MAP : sumsetB (SUM_MAP f g s) = IMAGE g (sumsetB s) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | sumsetB_SUM_MAP | null |
pairsetA_PAIR_MAP : pairsetA ((f ## g) p) = IMAGE f (pairsetA p) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | pairsetA_PAIR_MAP | null |
pairsetB_PAIR_MAP : pairsetB ((f ## g) p) = IMAGE g (pairsetB p) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | pairsetB_PAIR_MAP | null |
pairsetA_PAIR_MAP_o : pairsetA o (f ## g) = IMAGE f o pairsetA | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | pairsetA_PAIR_MAP_o | null |
pairsetB_PAIR_MAP_o : pairsetB o (f ## g) = IMAGE g o pairsetB | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | pairsetB_PAIR_MAP_o | null |
fmapset_o_f_o : FRANGE o (o_f) f = IMAGE f o FRANGE | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | fmapset_o_f_o | null |
fmapID : (o_f) (λx.x) = (λy.y) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | fmapID | null |
pairmapID : ((λx.x) ## (λy.y)) = (λp.p) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | pairmapID | null |
summapID : SUM_MAP (λx.x) (λy.y) = (λs.s) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | summapID | null |
listmapID : MAP (λe.e) = (λl.l) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | listmapID | null |
mapID0 : mapF (λx.x) (λy.y) = (λv.v) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | mapID0 | null |
pairmapO : (f1 ## f2) o (g1 ## g2) = (f1 o g1) ## (f2 o g2) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | pairmapO | null |
fmapO : (o_f) f o (o_f) g = (o_f) (f o g) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | fmapO | null |
mapO0 : mapF f1 f2 o mapF g1 g2 = mapF (f1 o g1) (f2 o g2) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | mapO0 | null |
setA_map : setAF (mapF f1 f2 (x:(α,β)F)) = IMAGE f1 (setAF x) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | setA_map | null |
setB_map : setBF (mapF f1 f2 x) = IMAGE f2 (setBF x) | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | setB_map | null |
SUM_MAP_CONG : (∀a. a ∈ sumsetA x ⇒ f1 a = f2 a) ∧ (∀b. b ∈ sumsetB x ⇒ g1 b = g2 b) ⇒ SUM_MAP f1 g1 x = SUM_MAP f2 g2 x | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | SUM_MAP_CONG | null |
FMAP_COMPOSE_CONG : (∀v. v ∈ FRANGE fm ⇒ f v = g v) ⇒ f o_f fm = g o_f fm | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | FMAP_COMPOSE_CONG | null |
PAIR_MAP_CONG : (∀a. a ∈ pairsetA p ⇒ f1 a = f2 a) ∧ (∀b. b ∈ pairsetB p ⇒ g1 b = g2 b) ⇒ (f1 ## g1) p = (f2 ## g2) p | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | PAIR_MAP_CONG | null |
map_CONG : (∀a. a ∈ setAF x ⇒ f1 a = f2 a) ∧ (∀b. b ∈ setBF x ⇒ g1 b = g2 b) ⇒ mapF f1 g1 x = mapF f2 g2 x | theorem | examples/bnf-datatypes | [] | examples/bnf-datatypes/concreteBNFScript.sml | map_CONG | null |
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