Nuprl Lemma : lifting-callbyvalue-atom_eq

[a,b,c,d,H:Top].
  (eval if a=b then else fi  in
   H[x] if a=b then eval in H[x] else eval in H[x] fi )


Proof




Definitions occuring in Statement :  callbyvalue: callbyvalue uall: [x:A]. B[x] top: Top so_apply: x[s] atom_eq: if a=b then else fi  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 has-value: (a)↓ prop: guard: {T} or: P ∨ Q squash: T
Lemmas referenced :  top_wf is-exception_wf base_wf has-value_wf_base lifting-strict-atom_eq
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 callbyvalueCallbyvalue hypothesis callbyvalueReduce baseApply closedConclusion hypothesisEquality callbyvalueExceptionCases inrFormation imageMemberEquality imageElimination exceptionSqequal inlFormation sqequalAxiom because_Cache

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



Date html generated: 2016_05_13-PM-03_42_28
Last ObjectModification: 2016_01_14-PM-07_08_46

Theory : computation


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