Nuprl Lemma : cosetTC_wf
∀[a:coSet{i:l}]. (cosetTC(a) ∈ coSet{i:l})
Proof
Definitions occuring in Statement :
cosetTC: cosetTC(a),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
prop: ℙ,
nat: ℕ,
subtype_rel: A ⊆r B,
coSet: coSet{i:l},
so_apply: x[s],
so_lambda: λ2x.t[x],
cosetTC: cosetTC(a),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
subtype_rel_self,
copath-at_wf,
nat_wf,
copath-length_wf,
less_than_wf,
copath_wf,
mk-coset_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
instantiate,
rename,
setElimination,
applyEquality,
because_Cache,
natural_numberEquality,
hypothesis,
hypothesisEquality,
lambdaEquality,
universeEquality,
setEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:coSet\{i:l\}]. (cosetTC(a) \mmember{} coSet\{i:l\})
Date html generated:
2018_07_29-AM-10_00_20
Last ObjectModification:
2018_07_18-PM-05_36_57
Theory : constructive!set!theory
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