Nuprl Lemma : setmem_functionality
∀x1,s1,x2,s2:coSet{i:l}. (seteq(x1;x2) ⇒ seteq(s1;s2) ⇒ {(x1 ∈ s1) ⇐⇒ (x2 ∈ s2)})
Proof
Definitions occuring in Statement :
setmem: (x ∈ s),
seteq: seteq(s1;s2),
coSet: coSet{i:l},
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
coSet_wf,
setmemfunc_wf
Rules used in proof :
because_Cache,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}x1,s1,x2,s2:coSet\{i:l\}. (seteq(x1;x2) {}\mRightarrow{} seteq(s1;s2) {}\mRightarrow{} \{(x1 \mmember{} s1) \mLeftarrow{}{}\mRightarrow{} (x2 \mmember{} s2)\})
Date html generated:
2018_07_29-AM-09_51_38
Last ObjectModification:
2018_07_11-PM-00_36_00
Theory : constructive!set!theory
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