Nuprl Lemma : lifting-apply-less

[n,m,a,b,c:Top].  (if (n) < (m)  then a  else if (n) < (m)  then c  else (b c))


Proof




Definitions occuring in Statement :  uall: [x:A]. B[x] top: Top less: if (a) < (b)  then c  else d apply: a 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 callbyvalueApply hypothesis baseApply closedConclusion hypothesisEquality applyExceptionCases inrFormation imageMemberEquality imageElimination exceptionSqequal inlFormation sqequalAxiom because_Cache

Latex:
\mforall{}[n,m,a,b,c:Top].    (if  (n)  <  (m)    then  a    else  b  c  \msim{}  if  (n)  <  (m)    then  a  c    else  (b  c))



Date html generated: 2016_05_13-PM-03_42_54
Last ObjectModification: 2016_01_14-PM-07_08_32

Theory : computation


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