Nuprl Lemma : pairset_functionality
∀a,b,a',b':coSet{i:l}. (seteq(a;a') ⇒ seteq(b;b') ⇒ seteq({a,b};{a',b'}))
Proof
Definitions occuring in Statement :
pairset: {a,b},
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
or: P ∨ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
coSet_wf,
setmem_wf,
setmem-pairset,
iff_wf,
seteq_weakening,
seteq_functionality,
seteq_wf,
or_wf,
pairset_wf,
co-seteq-iff
Rules used in proof :
impliesFunctionality,
orFunctionality,
addLevel,
because_Cache,
independent_pairFormation,
independent_functionElimination,
productElimination,
hypothesis,
hypothesisEquality,
isectElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}a,b,a',b':coSet\{i:l\}. (seteq(a;a') {}\mRightarrow{} seteq(b;b') {}\mRightarrow{} seteq(\{a,b\};\{a',b'\}))
Date html generated:
2018_07_29-AM-09_59_38
Last ObjectModification:
2018_07_18-AM-11_09_54
Theory : constructive!set!theory
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