Nuprl Lemma : fst-orderedpairset
∀a,b:coSet{i:l}. seteq(fst((a,b));a)
Proof
Definitions occuring in Statement :
orderedpair-fst: fst(pr),
orderedpairset: (a,b),
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x]
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
orderedpair-fst: fst(pr),
all: ∀x:A. B[x]
Lemmas referenced :
seteq_weakening,
orderedpair-first,
singleitem_functionality,
seteq_functionality,
singleitem-singleset,
singleset_wf,
orderedpairset_wf,
orderedpair-fsts_wf,
singleitem_wf,
coSet_wf
Rules used in proof :
productElimination,
independent_functionElimination,
dependent_functionElimination,
because_Cache,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}a,b:coSet\{i:l\}. seteq(fst((a,b));a)
Date html generated:
2018_07_29-AM-10_02_10
Last ObjectModification:
2018_07_18-PM-03_04_59
Theory : constructive!set!theory
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