### Nuprl Lemma : name_eq-normalize3

`∀[F,G,X,a,b:Top].`
`  (case name_eq(a;b) ∧b X of inl(x) => F[a] | inr(y) => G ~ case name_eq(a;b) ∧b X of inl(x) => F[b] | inr(y) => G)`

Proof

Definitions occuring in Statement :  name_eq: `name_eq(x;y)` band: `p ∧b q` 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 :  so_apply: `x[s]` uall: `∀[x:A]. B[x]` member: `t ∈ T`
Lemmas referenced :  name_eq-normalize2 top_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis because_Cache isect_memberFormation introduction sqequalAxiom sqequalRule isect_memberEquality

Latex:
\mforall{}[F,G,X,a,b:Top].
(case  name\_eq(a;b)  \mwedge{}\msubb{}  X  of  inl(x)  =>  F[a]  |  inr(y)  =>  G  \msim{}  case  name\_eq(a;b)  \mwedge{}\msubb{}  X
of  inl(x)  =>
F[b]
|  inr(y)  =>
G)

Date html generated: 2016_05_14-PM-03_34_52
Last ObjectModification: 2015_12_26-PM-05_59_50

Theory : decidable!equality

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