Nuprl Lemma : lifting-callbyvalueall-decide-name_eq
∀[a,b,F,G,H:Top].
(let x ⟵ case name_eq(a;b) of inl(x) => F[x] | inr(x) => H[x]
in G[x] ~ case name_eq(a;b) of inl(x) => let x ⟵ F[x] in G[x] | inr(x) => let x ⟵ H[x] in G[x])
Proof
Definitions occuring in Statement :
name_eq: name_eq(x;y),
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
lifting-callbyvalueall-decide,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalAxiom,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[a,b,F,G,H:Top].
(let x \mleftarrow{}{} case name\_eq(a;b) of inl(x) => F[x] | inr(x) => H[x]
in G[x] \msim{} case name\_eq(a;b) of inl(x) => let x \mleftarrow{}{} F[x] in G[x] | inr(x) => let x \mleftarrow{}{} H[x] in G[x])
Date html generated:
2016_05_15-PM-02_07_17
Last ObjectModification:
2015_12_27-AM-00_37_32
Theory : untyped!computation
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