Nuprl Lemma : hdf-with-state-pair-left-axiom
∀[L,S,G,init:Top]. ∀[m:ℕ].
(fix((λmk-hdf,s. (inl (λa.cbva_seq(L[s;a]; λg.<mk-hdf <Ax, S[s;a;g]>, G[s;a;g]>; m))))) <Ax, init> ~ fix((λmk-hdf,s. (\000Cinl (λa.cbva_seq(L[<Ax, s>;a]; λg.<mk-hdf S[<Ax, s>;a;g], G[<Ax, s>;a;g]>; m))))) init)
Proof
Definitions occuring in Statement :
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2;s3],
so_apply: x[s1;s2],
apply: f a,
fix: fix(F),
lambda: λx.A[x],
pair: <a, b>,
inl: inl x,
sqequal: s ~ t,
axiom: Ax,
cbva_seq: cbva_seq(L; F; m)
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
nat_wf,
top_wf,
fun_exp0_lemma,
strictness-apply,
bottom_diverge,
has-value_wf_base,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
fun_exp_unroll_1
\mforall{}[L,S,G,init:Top]. \mforall{}[m:\mBbbN{}].
(fix((\mlambda{}mk-hdf,s. (inl (\mlambda{}a.cbva\_seq(L[s;a]; \mlambda{}g.<mk-hdf <Ax, S[s;a;g]>, G[s;a;g]> m))))) <Ax, init>\000C \msim{} fix((\mlambda{}mk-hdf,s. (inl (\mlambda{}a.cbva\_seq(L[<Ax, s>a]; \mlambda{}g.<mk-hdf S[<Ax, s>a;g], G[<Ax, s>a;g]> m))))\000C) init)
Date html generated:
2015_07_17-AM-08_16_51
Last ObjectModification:
2015_01_27-AM-11_51_33
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