Nuprl Lemma : ball_cons_lemma
∀f,as,a,T:Top. (∀bx(:T) ∈ [a / as]. f[x] ~ f[a] ∧b (∀bx(:T) ∈ as. f[x]))
Proof
Definitions occuring in Statement :
ball: ball,
cons: [a / b],
band: p ∧b q,
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
ball: ball,
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
band_mon: <𝔹,∧b>,
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{}f,as,a,T:Top. (\mforall{}\msubb{}x(:T) \mmember{} [a / as]. f[x] \msim{} f[a] \mwedge{}\msubb{} (\mforall{}\msubb{}x(:T) \mmember{} as. f[x]))
Date html generated:
2016_05_16-AM-07_37_13
Last ObjectModification:
2015_12_28-PM-05_45_15
Theory : list_2
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