Nuprl Lemma : seteqweaken1
∀s1,s2:coSet{i:l}. ((s1 = s2 ∈ coSet{i:l}) ⇒ seteq(s1;s2))
Proof
Definitions occuring in Statement :
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
refl: Refl(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 :
seteq_wf,
and_wf,
coSet_wf,
equal_wf,
seteq-equiv
Rules used in proof :
rename,
setElimination,
applyLambdaEquality,
independent_pairFormation,
dependent_set_memberEquality,
sqequalRule,
equalitySymmetry,
hyp_replacement,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
isectElimination,
instantiate,
lambdaFormation,
thin,
productElimination,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}s1,s2:coSet\{i:l\}. ((s1 = s2) {}\mRightarrow{} seteq(s1;s2))
Date html generated:
2018_07_29-AM-09_50_52
Last ObjectModification:
2018_07_11-AM-11_47_14
Theory : constructive!set!theory
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