Nuprl Lemma : empty-fset-union
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[s:fset(T)]. ({} ⋃ s = s ∈ fset(T))
Proof
Definitions occuring in Statement :
empty-fset: {},
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],
top: Top,
or: P ∨ Q,
false: False,
implies: P ⇒ Q,
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
fset-extensionality,
fset-union_wf,
empty-fset_wf,
fset_wf,
deq_wf,
mem_empty_lemma,
fset-member_witness,
or_wf,
false_wf,
fset-member_wf,
member-fset-union,
uiff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
universeEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
independent_pairFormation,
unionElimination,
independent_functionElimination,
rename,
inrFormation,
addLevel,
cumulativity,
independent_pairEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[s:fset(T)]. (\{\} \mcup{} s = s)
Date html generated:
2016_05_14-PM-03_40_39
Last ObjectModification:
2015_12_26-PM-06_40_48
Theory : finite!sets
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