Nuprl Lemma : name_eq-normalize2

  (case name_eq(a;b) ∧b of inl(x) => inr(y) => case name_eq(a;b) ∧b of inl(x) => inr(y) => G)


Definitions occuring in Statement :  name_eq: name_eq(x;y) band: p ∧b q uall: [x:A]. B[x] top: Top apply: a decide: case of inl(x) => s[x] inr(y) => t[y] sqequal: t
Definitions unfolded in proof :  band: p ∧b q bfalse: ff uall: [x:A]. B[x] member: t ∈ T top: Top ifthenelse: if then else fi  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] 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 :  name_eq-normalize lifting-strict-decide top_wf equal_wf has-value_wf_base base_wf is-exception_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin isect_memberEquality voidElimination voidEquality hypothesisEquality sqequalRule baseClosed independent_isectElimination independent_pairFormation lambdaFormation callbyvalueDecide hypothesis equalityTransitivity equalitySymmetry unionEquality unionElimination sqleReflexivity dependent_functionElimination independent_functionElimination baseApply closedConclusion decideExceptionCases inrFormation because_Cache imageMemberEquality imageElimination exceptionSqequal inlFormation isect_memberFormation sqequalAxiom

    (case  name\_eq(a;b)  \mwedge{}\msubb{}  X  of  inl(x)  =>  F  a  |  inr(y)  =>  G  \msim{}  case  name\_eq(a;b)  \mwedge{}\msubb{}  X
      of  inl(x)  =>
      F  b
      |  inr(y)  =>

Date html generated: 2017_04_17-AM-09_17_32
Last ObjectModification: 2017_02_27-PM-05_21_48

Theory : decidable!equality

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