Nuprl Lemma : lifting-add-ispair-1

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


Proof




Definitions occuring in Statement :  uall: [x:A]. B[x] top: Top ispair: if is pair then otherwise b add: m 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 int-value-type value-type-has-value lifting-strict-ispair
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 callbyvalueAdd hypothesis baseApply closedConclusion hypothesisEquality productElimination because_Cache equalityTransitivity equalitySymmetry addExceptionCases exceptionSqequal inrFormation intEquality imageMemberEquality imageElimination inlFormation sqequalAxiom

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



Date html generated: 2016_05_13-PM-03_43_12
Last ObjectModification: 2016_01_14-PM-07_07_50

Theory : computation


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