Nuprl Lemma : subtype-bag-only
∀[T:Type]. ∀[bs:bag(T)]. bs ∈ bag({x:T| x = only(bs) ∈ T} ) supposing #(bs) = 1 ∈ ℤ
Proof
Definitions occuring in Statement :
bag-only: only(bs),
bag-size: #(bs),
bag: bag(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
single-bag: {x}
Lemmas referenced :
bag-size-one,
bag-only_wf,
equal_wf,
equal-wf-T-base,
bag-size_wf,
nat_wf,
bag_wf,
cons_wf,
nil_wf,
list-subtype-bag
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
cumulativity,
because_Cache,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
intEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
baseClosed,
isect_memberEquality,
universeEquality,
setEquality,
dependent_set_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[bs:bag(T)]. bs \mmember{} bag(\{x:T| x = only(bs)\} ) supposing \#(bs) = 1
Date html generated:
2017_10_01-AM-08_52_32
Last ObjectModification:
2017_07_26-PM-04_34_04
Theory : bags
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