Nuprl Lemma : normalization-callbyvalueall-spread1
∀[F,G,H,a:Top].
(let x ⟵ a
in F[x] let u,v = x in H[x;u;v] let y ⟵ u in G[x;u;v;y] ~ let x ⟵ a
in F[x] let u,v = x in H[x;u;v] G[x;u;v;u])
Proof
Definitions occuring in Statement :
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2;s3;s4],
so_apply: x[s1;s2;s3],
so_apply: x[s],
apply: f a,
spread: spread def,
sqequal: s ~ t
Definitions unfolded in proof :
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
has-valueall: has-valueall(a),
implies: P ⇒ Q,
prop: ℙ,
has-value: (a)↓,
uiff: uiff(P;Q),
and: P ∧ Q
Lemmas referenced :
top_wf,
is-exception_wf,
has-value_wf_base,
evalall-sqequal,
has-valueall-pair,
pair-eta,
has-valueall_wf_base,
cbv_sqequal
Rules used in proof :
cut,
sqequalRule,
thin,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
independent_isectElimination,
lambdaFormation,
hypothesis,
because_Cache,
sqequalSqle,
divergentSqle,
callbyvalueSpread,
equalityTransitivity,
equalitySymmetry,
productElimination,
callbyvalueReduce,
sqleReflexivity,
introduction,
spreadExceptionCases,
axiomSqleEquality,
exceptionSqequal,
isect_memberFormation,
sqequalAxiom,
isect_memberEquality
Latex:
\mforall{}[F,G,H,a:Top].
(let x \mleftarrow{}{} a
in F[x] let u,v = x in H[x;u;v] let y \mleftarrow{}{} u in G[x;u;v;y] \msim{} let x \mleftarrow{}{} a
in F[x]
let u,v = x
in H[x;u;v] G[x;u;v;u])
Date html generated:
2016_05_13-PM-04_08_27
Last ObjectModification:
2016_01_14-PM-07_46_05
Theory : fun_1
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