Nuprl Lemma : decidable__fset-member
∀[T:Type]. ∀eq:EqDecider(T). ∀x:fset(T). ∀a:T. Dec(a ∈ x)
Proof
Definitions occuring in Statement :
fset-member: a ∈ s,
fset: fset(T),
deq: EqDecider(T),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
fset_wf,
deq_wf,
fset-member_wf,
assert_wf,
deq-fset-member_wf,
decidable__assert,
decidable_functionality,
iff_weakening_uiff,
assert-deq-fset-member
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
hypothesisEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
universeEquality,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
productElimination,
independent_pairFormation
Latex:
\mforall{}[T:Type]. \mforall{}eq:EqDecider(T). \mforall{}x:fset(T). \mforall{}a:T. Dec(a \mmember{} x)
Date html generated:
2016_05_14-PM-03_38_33
Last ObjectModification:
2015_12_26-PM-06_42_12
Theory : finite!sets
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