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)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
nat_plus: ℕ+,
so_apply: x[s1;s2],
so_apply: x[s1;s2;s3]
Latex:
\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:
2016_05_16-AM-10_50_35
Last ObjectModification:
2016_01_17-AM-11_07_58
Theory : halting!dataflow
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