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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