Nuprl Lemma : lifting-decide-less

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

Proof

Definitions occuring in Statement :  uall: `∀[x:A]. B[x]` top: `Top` so_apply: `x[s]` less: `if (a) < (b)  then c  else d` 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]` so_lambda: `λ2x.t[x]` top: `Top` so_apply: `x[s]` 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`
Lemmas referenced :  lifting-strict-less top_wf equal_wf has-value_wf_base base_wf is-exception_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin baseClosed isect_memberEquality voidElimination voidEquality independent_isectElimination independent_pairFormation lambdaFormation callbyvalueDecide hypothesis hypothesisEquality equalityTransitivity equalitySymmetry unionEquality unionElimination sqleReflexivity dependent_functionElimination independent_functionElimination baseApply closedConclusion decideExceptionCases inrFormation because_Cache imageMemberEquality imageElimination exceptionSqequal inlFormation sqequalAxiom

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

Date html generated: 2017_04_14-AM-07_21_04
Last ObjectModification: 2017_02_27-PM-02_54_37

Theory : computation

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