### Nuprl Lemma : decide-decide3

`∀[x:Top + Top]. ∀[f1,f2,h:Top].`
`  (case x of inl(z) => h[z] | inr(z) => case x of inl(z) => f1[z] | inr(z) => f2[z] ~ case x`
`   of inl(z) =>`
`   h[z]`
`   | inr(z) =>`
`   f2[z])`

Proof

Definitions occuring in Statement :  uall: `∀[x:A]. B[x]` top: `Top` so_apply: `x[s]` decide: `case b of inl(x) => s[x] | inr(y) => t[y]` union: `left + right` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T`
Lemmas referenced :  top_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut unionElimination thin sqequalRule sqequalAxiom lemma_by_obid hypothesis sqequalHypSubstitution isect_memberEquality isectElimination hypothesisEquality because_Cache unionEquality

Latex:
\mforall{}[x:Top  +  Top].  \mforall{}[f1,f2,h:Top].
(case  x  of  inl(z)  =>  h[z]  |  inr(z)  =>  case  x  of  inl(z)  =>  f1[z]  |  inr(z)  =>  f2[z]  \msim{}  case  x
of  inl(z)  =>
h[z]
|  inr(z)  =>
f2[z])

Date html generated: 2016_05_15-PM-03_25_12
Last ObjectModification: 2015_12_27-PM-01_06_44

Theory : general

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