Nuprl Lemma : seteq_functionality
∀x1,x2,y1,y2:coSet{i:l}. (seteq(x1;x2) ⇒ seteq(y1;y2) ⇒ (seteq(x1;y1) ⇐⇒ seteq(x2;y2)))
Proof
Definitions occuring in Statement :
seteq: seteq(s1;s2),
coSet: coSet{i:l},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
member: t ∈ T,
and: P ∧ Q,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
coSet_wf,
seteq_wf,
seteq_transitivity,
seteq_inversion
Rules used in proof :
isectElimination,
hypothesis,
independent_functionElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}x1,x2,y1,y2:coSet\{i:l\}. (seteq(x1;x2) {}\mRightarrow{} seteq(y1;y2) {}\mRightarrow{} (seteq(x1;y1) \mLeftarrow{}{}\mRightarrow{} seteq(x2;y2)))
Date html generated:
2018_07_29-AM-09_51_26
Last ObjectModification:
2018_07_11-PM-00_18_02
Theory : constructive!set!theory
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