Nuprl Lemma : proddeq_reduce_lemma
∀v,u,y,x,b,a:Top. (proddeq(a;b) <x, y> <u, v> ~ (a x u) ∧b (b y v))
Proof
Definitions occuring in Statement :
proddeq: proddeq(a;b),
band: p ∧b q,
top: Top,
all: ∀x:A. B[x],
apply: f a,
pair: <a, b>,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
proddeq: proddeq(a;b),
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule
Latex:
\mforall{}v,u,y,x,b,a:Top. (proddeq(a;b) <x, y> <u, v> \msim{} (a x u) \mwedge{}\msubb{} (b y v))
Date html generated:
2016_05_14-AM-06_07_19
Last ObjectModification:
2015_12_26-AM-11_46_21
Theory : equality!deciders
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