Nuprl Lemma : fset-union-commutes
∀[A:Type]. ∀[eqa:EqDecider(A)]. ∀[x,y:fset(A)]. (x ⋃ y = y ⋃ x ∈ fset(A))
Proof
Definitions occuring in Statement :
fset-union: x ⋃ y,
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,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
or: P ∨ Q,
guard: {T},
prop: ℙ
Lemmas referenced :
fset-extensionality,
fset-union_wf,
member-fset-union,
fset-member_wf,
fset-member_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
because_Cache,
sqequalRule,
isect_memberEquality,
axiomEquality,
independent_pairFormation,
dependent_functionElimination,
independent_functionElimination,
unionElimination,
inrFormation,
inlFormation,
independent_pairEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[A:Type]. \mforall{}[eqa:EqDecider(A)]. \mforall{}[x,y:fset(A)]. (x \mcup{} y = y \mcup{} x)
Date html generated:
2016_05_14-PM-03_38_36
Last ObjectModification:
2015_12_26-PM-06_42_05
Theory : finite!sets
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