Nuprl Lemma : lifting-callbyvalueall-less

[a,b,c,d,H:Top].
  (let x ⟵ if (a) < (b)  then c  else d
   in H[x] if (a) < (b)  then let x ⟵ in H[x]  else let x ⟵ in H[x])


Proof




Definitions occuring in Statement :  callbyvalueall: callbyvalueall uall: [x:A]. B[x] top: Top so_apply: x[s] less: if (a) < (b)  then c  else d 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] so_lambda: λ2x.t[x] top: Top so_apply: x[s] uimplies: supposing a strict4: strict4(F) and: P ∧ Q all: x:A. B[x] implies:  Q prop: callbyvalueall: callbyvalueall evalall: evalall(t) guard: {T} or: P ∨ Q has-value: (a)↓ squash: T
Lemmas referenced :  top_wf is-exception-evalall is-exception_wf base_wf has-value_wf_base has-valueall-has-value has-valueall-if-has-value-callbyvalueall lifting-strict-less
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 hypothesisEquality baseApply closedConclusion hypothesis callbyvalueExceptionCases inrFormation callbyvalueCallbyvalue callbyvalueReduce imageMemberEquality imageElimination independent_functionElimination sqequalAxiom because_Cache

Latex:
\mforall{}[a,b,c,d,H:Top].
    (let  x  \mleftarrow{}{}  if  (a)  <  (b)    then  c    else  d
      in  H[x]  \msim{}  if  (a)  <  (b)    then  let  x  \mleftarrow{}{}  c  in  H[x]    else  let  x  \mleftarrow{}{}  d  in  H[x])



Date html generated: 2016_05_13-PM-03_42_33
Last ObjectModification: 2016_01_14-PM-07_08_23

Theory : computation


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