Nuprl Lemma : orderedpair-fst_wf
∀[pr:coSet{i:l}]. (fst(pr) ∈ coSet{i:l})
Proof
Definitions occuring in Statement :
orderedpair-fst: fst(pr),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
orderedpair-fst: fst(pr),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
orderedpair-fsts_wf,
singleitem_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[pr:coSet\{i:l\}]. (fst(pr) \mmember{} coSet\{i:l\})
Date html generated:
2018_07_29-AM-10_02_01
Last ObjectModification:
2018_07_18-PM-03_03_41
Theory : constructive!set!theory
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