Nuprl Lemma : productdeq_reduce_lemma
∀v,u,y,x,b,a,B,A:Top.  (product-deq(A;B;a;b) <x, y> <u, v> ~ (a x u) ∧b (b y v))
Proof
Definitions occuring in Statement : 
product-deq: product-deq(A;B;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
, 
product-deq: product-deq(A;B;a;b)
, 
top: Top
Lemmas referenced : 
top_wf, 
proddeq_reduce_lemma
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
hypothesis, 
lemma_by_obid, 
sqequalRule, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
isect_memberEquality, 
voidElimination, 
voidEquality
Latex:
\mforall{}v,u,y,x,b,a,B,A:Top.    (product-deq(A;B;a;b)  <x,  y>  <u,  v>  \msim{}  (a  x  u)  \mwedge{}\msubb{}  (b  y  v))
Date html generated:
2016_05_14-AM-06_07_25
Last ObjectModification:
2015_12_26-AM-11_46_38
Theory : equality!deciders
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