Nuprl Lemma : singleitem-singleset
∀a:coSet{i:l}. seteq(singleitem({a});a)
Proof
Definitions occuring in Statement :
singleitem: singleitem(s),
singleset: {a},
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x]
Definitions unfolded in proof :
guard: {T},
exists: ∃x:A. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
singleitem: singleitem(s),
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
setmem_functionality,
unionset_wf,
setmem-unionset,
iff_wf,
setmem-singleset,
seteq_weakening,
setmem_wf,
seteq_wf,
exists_wf,
coSet_wf,
singleset_wf,
singleitem_wf,
co-seteq-iff
Rules used in proof :
existsLevelFunctionality,
andLevelFunctionality,
existsFunctionality,
impliesFunctionality,
addLevel,
because_Cache,
dependent_pairFormation,
cumulativity,
productEquality,
lambdaEquality,
sqequalRule,
instantiate,
independent_pairFormation,
independent_functionElimination,
productElimination,
hypothesis,
hypothesisEquality,
isectElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}a:coSet\{i:l\}. seteq(singleitem(\{a\});a)
Date html generated:
2018_07_29-AM-09_59_24
Last ObjectModification:
2018_07_18-PM-03_03_29
Theory : constructive!set!theory
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