Nuprl Lemma : lifting-callbyvalueall-decide

[a,F,G,H:Top].
  (let x ⟵ case of inl(x) => F[x] inr(x) => H[x]
   in G[x] case of inl(x) => let x ⟵ F[x] in G[x] inr(x) => let x ⟵ H[x] in G[x])


Proof




Definitions occuring in Statement :  callbyvalueall: callbyvalueall uall: [x:A]. B[x] top: Top so_apply: x[s] 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] 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-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 hypothesisEquality baseApply closedConclusion hypothesis callbyvalueExceptionCases inrFormation callbyvalueCallbyvalue callbyvalueReduce imageMemberEquality imageElimination independent_functionElimination sqequalAxiom because_Cache

Latex:
\mforall{}[a,F,G,H:Top].
    (let  x  \mleftarrow{}{}  case  a  of  inl(x)  =>  F[x]  |  inr(x)  =>  H[x]
      in  G[x]  \msim{}  case  a  of  inl(x)  =>  let  x  \mleftarrow{}{}  F[x]  in  G[x]  |  inr(x)  =>  let  x  \mleftarrow{}{}  H[x]  in  G[x])



Date html generated: 2016_05_13-PM-03_42_38
Last ObjectModification: 2016_01_14-PM-07_08_16

Theory : computation


Home Index