Nuprl Lemma : singleset_wf
∀[a:coSet{i:l}]. ({a} ∈ coSet{i:l})
Proof
Definitions occuring in Statement :
singleset: {a},
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
mk-coset: mk-coset(T;f),
singleset: {a},
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
unit_wf2,
mk-coset_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesisEquality,
lambdaEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:coSet\{i:l\}]. (\{a\} \mmember{} coSet\{i:l\})
Date html generated:
2018_07_29-AM-09_53_12
Last ObjectModification:
2018_07_18-AM-10_45_05
Theory : constructive!set!theory
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