Nuprl Lemma : single-bags-equal
∀[T:Type]. ∀[x,y:T]. uiff({x} = {y} ∈ bag(T);x = y ∈ T)
Proof
Definitions occuring in Statement :
single-bag: {x},
bag: bag(T),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x]
Lemmas referenced :
bag-member-single,
bag-member_wf,
equal_wf,
bag_wf,
single-bag_wf,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
productElimination,
independent_isectElimination,
equalitySymmetry,
hypothesis,
hyp_replacement,
Error :applyLambdaEquality,
cumulativity,
sqequalRule,
dependent_functionElimination,
dependent_set_memberEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity
Latex:
\mforall{}[T:Type]. \mforall{}[x,y:T]. uiff(\{x\} = \{y\};x = y)
Date html generated:
2016_10_25-AM-10_27_20
Last ObjectModification:
2016_07_12-AM-06_43_29
Theory : bags
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