### Nuprl Lemma : band-simple-decide

`∀[a,b:Top].  (case a of inl(y) => inl ⋅ | inr(z) => inr ⋅  ∧b b ~ case a of inl(y) => b | inr(z) => inr ⋅ )`

Proof

Definitions occuring in Statement :  band: `p ∧b q` it: `⋅` uall: `∀[x:A]. B[x]` top: `Top` decide: `case b of inl(x) => s[x] | inr(y) => t[y]` inr: `inr x ` inl: `inl x` sqequal: `s ~ t`
Definitions unfolded in proof :  top: `Top` it: `⋅` band: `p ∧b q` uall: `∀[x:A]. B[x]` bfalse: `ff` ifthenelse: `if b then t else f fi ` so_lambda: `so_lambda(x,y,z,w.t[x; y; z; w])` member: `t ∈ T` so_apply: `x[s1;s2;s3;s4]` so_lambda: `λ2x.t[x]` 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-decide top_wf equal_wf has-value_wf_base base_wf is-exception_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalTransitivity computationStep sqequalReflexivity cut introduction 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 isect_memberFormation sqequalAxiom isectEquality

Latex:
\mforall{}[a,b:Top].
(case  a  of  inl(y)  =>  inl  \mcdot{}  |  inr(z)  =>  inr  \mcdot{}    \mwedge{}\msubb{}  b  \msim{}  case  a  of  inl(y)  =>  b  |  inr(z)  =>  inr  \mcdot{}  )

Date html generated: 2017_10_01-AM-08_39_29
Last ObjectModification: 2017_07_26-PM-04_27_32

Theory : untyped!computation

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