Nuprl Lemma : fset-intersection-commutes
∀[A:Type]. ∀[eqa:EqDecider(A)]. ∀[x,y:fset(A)]. (x ⋂ y = y ⋂ x ∈ fset(A))
Proof
Definitions occuring in Statement :
fset-intersection: a ⋂ b,
fset: fset(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
fset-extensionality,
fset-intersection_wf,
fset-member_witness,
fset-member_wf,
uiff_wf,
iff_weakening_uiff,
member-fset-intersection
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
because_Cache,
sqequalRule,
isect_memberEquality,
axiomEquality,
independent_pairFormation,
independent_pairEquality,
independent_functionElimination,
productEquality,
cumulativity,
addLevel
Latex:
\mforall{}[A:Type]. \mforall{}[eqa:EqDecider(A)]. \mforall{}[x,y:fset(A)]. (x \mcap{} y = y \mcap{} x)
Date html generated:
2019_06_20-PM-01_59_01
Last ObjectModification:
2018_08_24-PM-11_37_52
Theory : finite!sets
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