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
Home
Index