Nuprl Lemma : count_cons_lemma
∀bs,b,a,s:Top. (a #∈ [b / bs] ~ b2i(b (=b) a) + (a #∈ bs))
Proof
Definitions occuring in Statement :
count: a #∈ as,
cons: [a / b],
b2i: b2i(b),
top: Top,
infix_ap: x f y,
all: ∀x:A. B[x],
add: n + m,
sqequal: s ~ t,
set_eq: =b
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
count: a #∈ as,
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
int_add_grp: <ℤ+>,
grp_op: *,
pi2: snd(t),
pi1: fst(t),
infix_ap: x f y
Lemmas referenced :
top_wf,
mon_for_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{}bs,b,a,s:Top. (a \#\mmember{} [b / bs] \msim{} b2i(b (=\msubb{}) a) + (a \#\mmember{} bs))
Date html generated:
2016_05_16-AM-07_39_28
Last ObjectModification:
2015_12_28-PM-05_43_29
Theory : list_2
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