Nuprl Lemma : callbyvalueall_seq-spread0
∀[F,G,H,L:Top]. ∀[m:ℕ].
(let x,y = callbyvalueall_seq(L;λx.x;λg.<F[g], G[g]>;0;m)
in H[x;y] ~ callbyvalueall_seq(L;λx.x;λg.H[F[g];G[g]];0;m))
Proof
Definitions occuring in Statement :
callbyvalueall_seq: callbyvalueall_seq(L;G;F;n;m),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
so_apply: x[s],
lambda: λx.A[x],
spread: spread def,
pair: <a, b>,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
mk_applies: mk_applies(F;G;m),
all: ∀x:A. B[x]
Lemmas referenced :
callbyvalueall_seq-spread,
false_wf,
le_wf,
primrec0_lemma,
nat_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
dependent_functionElimination,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[F,G,H,L:Top]. \mforall{}[m:\mBbbN{}].
(let x,y = callbyvalueall\_seq(L;\mlambda{}x.x;\mlambda{}g.<F[g], G[g]>0;m)
in H[x;y] \msim{} callbyvalueall\_seq(L;\mlambda{}x.x;\mlambda{}g.H[F[g];G[g]];0;m))
Date html generated:
2016_05_15-PM-02_13_14
Last ObjectModification:
2015_12_27-AM-00_33_30
Theory : untyped!computation
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