### Nuprl Lemma : lifting-isaxiom-decide

`∀[a,b,c,F,G:Top].`
`  (if case a of inl(x) => F[x] | inr(x) => G[x] = Ax then b otherwise c ~ case a`
`   of inl(x) =>`
`   if F[x] = Ax then b otherwise c`
`   | inr(x) =>`
`   if G[x] = Ax then b otherwise c)`

Proof

Definitions occuring in Statement :  uall: `∀[x:A]. B[x]` top: `Top` so_apply: `x[s]` isaxiom: `if z = Ax then a otherwise b` 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` so_lambda: `so_lambda(x,y,z,w.t[x; y; z; w])` so_apply: `x[s1;s2;s3;s4]` top: `Top` uimplies: `b supposing a` strict4: `strict4(F)` and: `P ∧ Q` all: `∀x:A. B[x]` implies: `P `` Q` has-value: `(a)↓` prop: `ℙ` guard: `{T}` or: `P ∨ Q` squash: `↓T` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  top_wf is-exception_wf base_wf has-value_wf_base lifting-strict-decide
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin baseClosed isect_memberEquality voidElimination voidEquality independent_isectElimination independent_pairFormation lambdaFormation callbyvalueIsaxiom hypothesis baseApply closedConclusion hypothesisEquality isaxiomExceptionCases inrFormation imageMemberEquality imageElimination exceptionSqequal inlFormation sqequalAxiom because_Cache

Latex:
\mforall{}[a,b,c,F,G:Top].
(if  case  a  of  inl(x)  =>  F[x]  |  inr(x)  =>  G[x]  =  Ax  then  b  otherwise  c  \msim{}  case  a
of  inl(x)  =>
if  F[x]  =  Ax  then  b  otherwise  c
|  inr(x)  =>
if  G[x]  =  Ax  then  b  otherwise  c)

Date html generated: 2016_05_13-PM-03_42_18
Last ObjectModification: 2016_01_14-PM-07_08_43

Theory : computation

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