Nuprl Lemma : lifting-ispair-isaxiom2
∀[a,b,c,d,e:Top].
(if if a = Ax then b otherwise c is a pair then d otherwise e
~ if a = Ax then if b is a pair then d otherwise e otherwise if c is a pair then d otherwise e)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
ispair: if z is a pair then a otherwise b,
isaxiom: if z = Ax then a otherwise b,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
lifting-ispair-isaxiom,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalAxiom,
sqequalRule,
isect_memberEquality,
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_06
Last ObjectModification:
2015_12_26-AM-09_53_21
Theory : computation
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