Nuprl Lemma : orderedpair-fst_functionality
∀a,b:coSet{i:l}. (seteq(a;b) ⇒ seteq(fst(a);fst(b)))
Proof
Definitions occuring in Statement :
orderedpair-fst: fst(pr),
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
prop: ℙ,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
orderedpair-fst: fst(pr),
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
coSet_wf,
seteq_wf,
seteq_weakening,
orderedpair-fsts_functionality,
singleitem_functionality,
orderedpair-fsts_wf,
singleitem_wf,
seteq_functionality
Rules used in proof :
productElimination,
independent_functionElimination,
because_Cache,
hypothesis,
hypothesisEquality,
isectElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
sqequalRule,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}a,b:coSet\{i:l\}. (seteq(a;b) {}\mRightarrow{} seteq(fst(a);fst(b)))
Date html generated:
2018_07_29-AM-10_02_06
Last ObjectModification:
2018_07_18-PM-03_04_35
Theory : constructive!set!theory
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