Nuprl Lemma : seteqtrans1_ext
∀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 :
coW-equiv_transitivity,
coW-equiv-equiv_rel,
seteq-equiv,
seteqtrans1,
member: t ∈ T
Lemmas referenced :
seteqtrans1,
coW-equiv_transitivity,
coW-equiv-equiv_rel,
seteq-equiv
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
sqequalHypSubstitution,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
instantiate,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
introduction
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_15
Last ObjectModification:
2018_07_11-PM-00_13_51
Theory : constructive!set!theory
Home
Index