Nuprl Lemma : assert-deq-fset-member
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[a:T]. ∀[s:fset(T)]. uiff(↑a ∈b s;a ∈ s)
Proof
Definitions occuring in Statement :
deq-fset-member: a ∈b s,
fset-member: a ∈ s,
fset: fset(T),
deq: EqDecider(T),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
fset-member: a ∈ s,
deq-fset-member: a ∈b s,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
assert_witness,
deq-fset-member_wf,
assert_wf,
fset-member_wf,
fset_wf,
deq_wf,
fset-member_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
isect_memberFormation,
introduction,
cut,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_functionElimination,
because_Cache,
universeEquality,
sqequalRule,
productElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[a:T]. \mforall{}[s:fset(T)]. uiff(\muparrow{}a \mmember{}\msubb{} s;a \mmember{} s)
Date html generated:
2016_05_14-PM-03_38_10
Last ObjectModification:
2015_12_26-PM-06_42_17
Theory : finite!sets
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