Nuprl Lemma : filter_tt
∀[L:Top List]. (filter(λx.tt;L) ~ L)
Proof
Definitions occuring in Statement :
filter: filter(P;l),
list: T List,
btrue: tt,
uall: ∀[x:A]. B[x],
top: Top,
lambda: λx.A[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_apply: x[s],
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
l_all: (∀x∈L.P[x]),
all: ∀x:A. B[x],
true: True
Lemmas referenced :
filter_trivial,
top_wf,
btrue_wf,
list_wf,
int_seg_wf,
length_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
hypothesisEquality,
independent_isectElimination,
sqequalAxiom,
lambdaFormation,
natural_numberEquality
Latex:
\mforall{}[L:Top List]. (filter(\mlambda{}x.tt;L) \msim{} L)
Date html generated:
2016_05_14-AM-06_50_40
Last ObjectModification:
2015_12_26-PM-00_22_36
Theory : list_0
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