Nuprl Lemma : orderedpair-snds_functionality
∀a,b:coSet{i:l}. (seteq(a;b) ⇒ seteq(snds(a);snds(b)))
Proof
Definitions occuring in Statement :
orderedpair-snds: snds(pr),
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
set-predicate: set-predicate{i:l}(s;a.P[a]),
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
orderedpair-snds: snds(pr),
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
orderedpair-fst_functionality,
unionset_functionality,
setmem_functionality,
iff_wf,
all_wf,
orderedpairset_functionality,
seteq_weakening,
seteq_functionality,
setmem-sub-coset,
setmem_wf,
orderedpair-fst_wf,
orderedpairset_wf,
unionset_wf,
sub-set_wf,
co-seteq-iff,
coSet_wf,
seteq_wf
Rules used in proof :
andLevelFunctionality,
productEquality,
instantiate,
because_Cache,
impliesFunctionality,
independent_pairFormation,
allFunctionality,
addLevel,
independent_functionElimination,
productElimination,
cumulativity,
setEquality,
rename,
setElimination,
lambdaEquality,
sqequalRule,
dependent_functionElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}a,b:coSet\{i:l\}. (seteq(a;b) {}\mRightarrow{} seteq(snds(a);snds(b)))
Date html generated:
2018_07_29-AM-10_02_19
Last ObjectModification:
2018_07_18-PM-03_16_05
Theory : constructive!set!theory
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