Nuprl Lemma : decide-simple-int_eq

[a,b,c,d:Top].  (case if a=b  then inl ⋅  else (inr ⋅ of inl() => inr() => if a=b  then c  else d)


Proof




Definitions occuring in Statement :  it: uall: [x:A]. B[x] top: Top int_eq: if a=b  then c  else d 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: uall: [x:A]. B[x] 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-int_eq 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,c,d:Top].
    (case  if  a=b    then  inl  \mcdot{}    else  (inr  \mcdot{}  )  of  inl()  =>  c  |  inr()  =>  d  \msim{}  if  a=b    then  c    else  d)



Date html generated: 2017_10_01-AM-08_39_30
Last ObjectModification: 2017_07_26-PM-04_27_33

Theory : untyped!computation


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