Nuprl Lemma : lifting-isaxiom-spread

[a,b,c,F:Top].  (if let x,y in F[x;y] Ax then otherwise let x,y in if F[x;y] Ax then otherwise c)


Proof




Definitions occuring in Statement :  uall: [x:A]. B[x] top: Top so_apply: x[s1;s2] isaxiom: if Ax then otherwise b spread: spread def 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: λ2y.t[x; y] so_apply: x[s1;s2]
Lemmas referenced :  top_wf is-exception_wf base_wf has-value_wf_base lifting-strict-spread
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

Latex:
\mforall{}[a,b,c,F:Top].
    (if  let  x,y  =  a 
            in  F[x;y]  =  Ax  then  b  otherwise  c  \msim{}  let  x,y  =  a 
                                                                                    in  if  F[x;y]  =  Ax  then  b  otherwise  c)



Date html generated: 2016_05_13-PM-03_42_17
Last ObjectModification: 2016_01_14-PM-07_08_41

Theory : computation


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