Nuprl Lemma : lifting-ispair-isaxiom

[a,b,c,d,e:Top].
  (if if Ax then otherwise is pair then otherwise 
  if Ax then if is pair then otherwise otherwise if is pair then otherwise e)


Proof




Definitions occuring in Statement :  uall: [x:A]. B[x] top: Top ispair: if is pair then otherwise b isaxiom: if Ax then otherwise b 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-isaxiom
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 callbyvalueIspair hypothesis baseApply closedConclusion hypothesisEquality ispairExceptionCases inrFormation imageMemberEquality imageElimination exceptionSqequal inlFormation sqequalAxiom because_Cache

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



Date html generated: 2016_05_13-PM-03_42_05
Last ObjectModification: 2016_01_14-PM-07_08_50

Theory : computation


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