Nuprl Lemma : deq_member_cons_lemma
∀v,u,x,eq:Top. (x ∈b [u / v] ~ (eq u x) ∨bx ∈b v)
Proof
Definitions occuring in Statement :
deq-member: x ∈b L,
cons: [a / b],
bor: p ∨bq,
top: Top,
all: ∀x:A. B[x],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
deq-member: x ∈b L,
top: Top
Lemmas referenced :
top_wf,
reduce_cons_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,x,eq:Top. (x \mmember{}\msubb{} [u / v] \msim{} (eq u x) \mvee{}\msubb{}x \mmember{}\msubb{} v)
Date html generated:
2016_05_14-AM-06_53_08
Last ObjectModification:
2015_12_26-PM-00_20_36
Theory : list_0
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