Nuprl Lemma : maximal-sub-bag_wf
∀[T:Type]. ∀[b,m:bag(T)]. ∀[P:bag(T) ⟶ ℙ]. (maximal-sub-bag(T;m;b;s.P[s]) ∈ ℙ)
Proof
Definitions occuring in Statement :
maximal-sub-bag: maximal-sub-bag(T;m;b;s.P[s]),
bag: bag(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
so_apply: x[s],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
and: P ∧ Q,
prop: ℙ,
maximal-sub-bag: maximal-sub-bag(T;m;b;s.P[s]),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
sub-bag_wf,
bag_wf,
all_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
universeEquality,
functionExtensionality,
applyEquality,
functionEquality,
lambdaEquality,
hypothesis,
hypothesisEquality,
cumulativity,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[b,m:bag(T)]. \mforall{}[P:bag(T) {}\mrightarrow{} \mBbbP{}]. (maximal-sub-bag(T;m;b;s.P[s]) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-06_24_43
Last ObjectModification:
2018_01_08-AM-00_34_54
Theory : bags
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