Nuprl Lemma : empty-fset-ac-le
∀[eq,a:Top]. (fset-ac-le(eq;{};a) ~ True)
Proof
Definitions occuring in Statement :
fset-ac-le: fset-ac-le(eq;ac1;ac2),
empty-fset: {},
uall: ∀[x:A]. B[x],
top: Top,
true: True,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fset-ac-le: fset-ac-le(eq;ac1;ac2),
fset-all: fset-all(s;x.P[x]),
assert: ↑b,
ifthenelse: if b then t else f fi ,
fset-null: fset-null(s),
null: null(as),
fset-filter: {x ∈ s | P[x]},
filter: filter(P;l),
reduce: reduce(f;k;as),
list_ind: list_ind,
true: True,
empty-fset: {},
nil: [],
it: ⋅,
btrue: tt
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[eq,a:Top]. (fset-ac-le(eq;\{\};a) \msim{} True)
Date html generated:
2016_05_14-PM-03_43_03
Last ObjectModification:
2016_01_07-PM-04_46_02
Theory : finite!sets
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