Nuprl Lemma : seteqtrans1
∀s1,s2,s3:coSet{i:l}. (seteq(s1;s2) ⇒ seteq(s2;s3) ⇒ seteq(s1;s3))
Proof
Definitions occuring in Statement :
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
trans: Trans(T;x,y.E[x; y]),
guard: {T},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
and: P ∧ Q,
equiv_rel: EquivRel(T;x,y.E[x; y])
Lemmas referenced :
coSet_wf,
seteq_wf,
seteq-equiv
Rules used in proof :
independent_functionElimination,
dependent_functionElimination,
hypothesis,
hypothesisEquality,
isectElimination,
lambdaFormation,
thin,
productElimination,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}s1,s2,s3:coSet\{i:l\}. (seteq(s1;s2) {}\mRightarrow{} seteq(s2;s3) {}\mRightarrow{} seteq(s1;s3))
Date html generated:
2018_07_29-AM-09_51_13
Last ObjectModification:
2018_07_11-PM-00_09_07
Theory : constructive!set!theory
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