Nuprl Lemma : seteqweaken_wf
∀s1,s2:coSet{i:l}. (seteqweaken(s2) ∈ (s1 = s2 ∈ coSet{i:l}) ⇒ seteq(s1;s2))
Proof
Definitions occuring in Statement :
seteqweaken: seteqweaken(s2),
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
equal: s = t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
seteqweaken1_ext,
seteqweaken: seteqweaken(s2),
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
seteq_wf,
equal_wf,
all_wf,
coSet_wf,
subtype_rel_self,
seteqweaken1_ext
Rules used in proof :
cumulativity,
hypothesisEquality,
lambdaEquality,
functionEquality,
isectElimination,
sqequalHypSubstitution,
introduction,
hypothesis,
extract_by_obid,
instantiate,
thin,
applyEquality,
sqequalRule,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}s1,s2:coSet\{i:l\}. (seteqweaken(s2) \mmember{} (s1 = s2) {}\mRightarrow{} seteq(s1;s2))
Date html generated:
2018_07_29-AM-09_50_59
Last ObjectModification:
2018_07_11-PM-00_01_06
Theory : constructive!set!theory
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