Nuprl Lemma : band-simple-decide

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


Definitions occuring in Statement :  band: p ∧b q it: uall: [x:A]. B[x] top: Top decide: case of inl(x) => s[x] inr(y) => t[y] inr: inr  inl: inl x sqequal: t
Definitions unfolded in proof :  top: Top it: band: p ∧b q uall: [x:A]. B[x] bfalse: ff ifthenelse: if then else 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: supposing a strict4: strict4(F) and: P ∧ Q all: x:A. B[x] implies:  Q has-value: (a)↓ prop: 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

    (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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