Nuprl Lemma : lifting-isaxiom-decide

  (if case of inl(x) => F[x] inr(x) => G[x] Ax then otherwise case a
   of inl(x) =>
   if F[x] Ax then otherwise c
   inr(x) =>
   if G[x] Ax then otherwise c)


Definitions occuring in Statement :  uall: [x:A]. B[x] top: Top so_apply: x[s] isaxiom: if Ax then otherwise b decide: case of inl(x) => s[x] inr(y) => t[y] sqequal: 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] top: Top 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 so_lambda: λ2x.t[x] so_apply: x[s]
Lemmas referenced :  top_wf is-exception_wf base_wf has-value_wf_base lifting-strict-decide
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin baseClosed isect_memberEquality voidElimination voidEquality independent_isectElimination independent_pairFormation lambdaFormation callbyvalueIsaxiom hypothesis baseApply closedConclusion hypothesisEquality isaxiomExceptionCases inrFormation imageMemberEquality imageElimination exceptionSqequal inlFormation sqequalAxiom because_Cache

    (if  case  a  of  inl(x)  =>  F[x]  |  inr(x)  =>  G[x]  =  Ax  then  b  otherwise  c  \msim{}  case  a
      of  inl(x)  =>
      if  F[x]  =  Ax  then  b  otherwise  c
      |  inr(x)  =>
      if  G[x]  =  Ax  then  b  otherwise  c)

Date html generated: 2016_05_13-PM-03_42_18
Last ObjectModification: 2016_01_14-PM-07_08_43

Theory : computation

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