Nuprl Lemma : setTC-cosetTC
∀a:Set{i:l}. seteq(setTC(a);cosetTC(a))
Proof
Definitions occuring in Statement :
setTC: setTC(a),
cosetTC: cosetTC(a),
Set: Set{i:l},
seteq: seteq(s1;s2),
all: ∀x:A. B[x]
Definitions unfolded in proof :
prop: ℙ,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
Set_wf,
coSet_wf,
setsubset_wf,
transitive-set_wf,
setTC-least,
setTC-transitive,
setTC-contains,
set-subtype-coSet,
cosetTC-unique
Rules used in proof :
independent_functionElimination,
sqequalRule,
applyEquality,
hypothesis,
hypothesisEquality,
isectElimination,
because_Cache,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}a:Set\{i:l\}. seteq(setTC(a);cosetTC(a))
Date html generated:
2018_07_29-AM-10_03_46
Last ObjectModification:
2018_07_18-PM-08_57_42
Theory : constructive!set!theory
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