Nuprl Lemma : cosetTC_functionality
∀a,b:coSet{i:l}. (seteq(a;b) ⇒ seteq(cosetTC(a);cosetTC(b)))
Proof
Definitions occuring in Statement :
cosetTC: cosetTC(a),
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
cand: A c∧ B,
and: P ∧ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
seteq_wf,
cosetTC_wf,
seteq-iff-setsubset,
coSet_wf,
setsubset_wf,
cosetTC_functionality_subset
Rules used in proof :
functionEquality,
lambdaEquality,
sqequalRule,
instantiate,
cumulativity,
impliesFunctionality,
allFunctionality,
addLevel,
isectElimination,
productEquality,
independent_pairFormation,
hypothesis,
independent_functionElimination,
hypothesisEquality,
dependent_functionElimination,
extract_by_obid,
introduction,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
cut
Latex:
\mforall{}a,b:coSet\{i:l\}. (seteq(a;b) {}\mRightarrow{} seteq(cosetTC(a);cosetTC(b)))
Date html generated:
2018_07_29-AM-10_01_41
Last ObjectModification:
2018_07_18-PM-05_58_03
Theory : constructive!set!theory
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