Nuprl Lemma : lifting-add-isaxiom-2
∀[a:ℤ]. ∀[b,c,d:Top]. (a + if b = Ax then c otherwise d ~ if b = Ax then a + c otherwise a + d)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
isaxiom: if z = Ax then a otherwise b,
add: n + m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
add-commutes,
lifting-add-isaxiom-1,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalAxiom,
intEquality
Latex:
\mforall{}[a:\mBbbZ{}]. \mforall{}[b,c,d:Top]. (a + if b = Ax then c otherwise d \msim{} if b = Ax then a + c otherwise a + d)
Date html generated:
2016_05_13-PM-03_43_17
Last ObjectModification:
2015_12_26-AM-09_52_30
Theory : computation
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