Nuprl Lemma : mem_cons_lemma
∀bs,b,a,s:Top. (a ∈b [b / bs] ~ (b (=b) a) ∨b(a ∈b bs))
Proof
Definitions occuring in Statement :
mem: a ∈b as,
cons: [a / b],
bor: p ∨bq,
top: Top,
infix_ap: x f y,
all: ∀x:A. B[x],
sqequal: s ~ t,
set_eq: =b
Definitions unfolded in proof :
all: ∀x:A. B[x],
mem: a ∈b as,
mon_for: For{g} x ∈ as. f[x],
for: For{T,op,id} x ∈ as. f[x],
bor_mon: <𝔹,∨b>,
grp_op: *,
pi2: snd(t),
pi1: fst(t),
grp_id: e,
member: t ∈ T,
top: Top,
tlambda: λx:T. b[x]
Lemmas referenced :
map_cons_lemma,
reduce_cons_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis
Latex:
\mforall{}bs,b,a,s:Top. (a \mmember{}\msubb{} [b / bs] \msim{} (b (=\msubb{}) a) \mvee{}\msubb{}(a \mmember{}\msubb{} bs))
Date html generated:
2016_05_16-AM-07_36_57
Last ObjectModification:
2015_12_28-PM-05_45_21
Theory : list_2
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