Nuprl Lemma : lifting-isaxiom-less

[a,b,c,d,e,f:Top].
  (if if (a) < (b)  then c  else Ax then otherwise if (a) < (b)
                                                                then if Ax then otherwise f
                                                                else if Ax then otherwise f)


Proof




Definitions occuring in Statement :  uall: [x:A]. B[x] top: Top isaxiom: if Ax then otherwise b 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] 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
Lemmas referenced :  top_wf is-exception_wf base_wf has-value_wf_base 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 callbyvalueIsaxiom hypothesis baseApply closedConclusion hypothesisEquality isaxiomExceptionCases inrFormation imageMemberEquality imageElimination exceptionSqequal inlFormation sqequalAxiom because_Cache

Latex:
\mforall{}[a,b,c,d,e,f:Top].
    (if  if  (a)  <  (b)    then  c    else  d  =  Ax  then  e  otherwise  f  \msim{}  if  (a)  <  (b)
                                                                                                                                then  if  c  =  Ax  then  e  otherwise  f
                                                                                                                                else  if  d  =  Ax  then  e  otherwise  f)



Date html generated: 2016_05_13-PM-03_42_16
Last ObjectModification: 2016_01_14-PM-07_08_42

Theory : computation


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