Nuprl Lemma : decide-spread

  (case let a,b in F[a;b] of inl(u) => G[u] inr(v) => H[v] let a,b 
                                                                   in case F[a;b] of inl(u) => G[u] inr(v) => H[v])


Definitions occuring in Statement :  uall: [x:A]. B[x] top: Top so_apply: x[s1;s2] so_apply: x[s] spread: spread def decide: case of inl(x) => s[x] inr(y) => t[y] sqequal: t
Definitions unfolded in proof :  uall: [x:A]. B[x] top: Top so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]) member: t ∈ T 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 so_lambda: λ2y.t[x; y] so_apply: x[s1;s2]
Lemmas referenced :  lifting-strict-spread top_wf equal_wf has-value_wf_base base_wf is-exception_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalTransitivity computationStep sqequalReflexivity cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin baseClosed isect_memberEquality voidElimination voidEquality independent_isectElimination independent_pairFormation lambdaFormation callbyvalueDecide hypothesis hypothesisEquality equalityTransitivity equalitySymmetry unionEquality unionElimination sqleReflexivity dependent_functionElimination independent_functionElimination baseApply closedConclusion decideExceptionCases inrFormation because_Cache imageMemberEquality imageElimination exceptionSqequal inlFormation isect_memberFormation sqequalAxiom isectEquality

    (case  let  a,b  =  p  in  F[a;b]  of  inl(u)  =>  G[u]  |  inr(v)  =>  H[v]  \msim{}  let  a,b  =  p 
                                                                                                                                      in  case  F[a;b]
                                                                                                                                              of  inl(u)  =>
                                                                                                                                              |  inr(v)  =>

Date html generated: 2017_10_01-AM-08_39_26
Last ObjectModification: 2017_07_26-PM-04_27_29

Theory : untyped!computation

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