Nuprl Lemma : bag-member-single-weak
∀[T:Type]. ∀[x,y:T]. (x ↓∈ {y} ⇐⇒ x = y ∈ T)
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
single-bag: {x},
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
bag-member: x ↓∈ bs,
squash: ↓T
Lemmas referenced :
bag-member-single,
bag-member_wf,
single-bag_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
cumulativity,
dependent_functionElimination,
sqequalRule,
independent_pairEquality,
lambdaEquality,
axiomEquality,
imageElimination,
imageMemberEquality,
baseClosed,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x,y:T]. (x \mdownarrow{}\mmember{} \{y\} \mLeftarrow{}{}\mRightarrow{} x = y)
Date html generated:
2017_10_01-AM-08_53_35
Last ObjectModification:
2017_07_26-PM-04_35_19
Theory : bags
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