Nuprl Lemma : bl-exists-cons
∀[f,u,v:Top]. ((∃x∈[u / v].f[x])_b ~ f[u] ∨b(∃x∈v.f[x])_b)
Proof
Definitions occuring in Statement :
bl-exists: (∃x∈L.P[x])_b,
cons: [a / b],
bor: p ∨bq,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
sqequal: s ~ t
Definitions unfolded in proof :
bl-exists: (∃x∈L.P[x])_b,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x]
Lemmas referenced :
reduce_cons_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[f,u,v:Top]. ((\mexists{}x\mmember{}[u / v].f[x])\_b \msim{} f[u] \mvee{}\msubb{}(\mexists{}x\mmember{}v.f[x])\_b)
Date html generated:
2016_05_14-PM-02_10_36
Last ObjectModification:
2015_12_26-PM-05_04_15
Theory : list_1
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