Nuprl Lemma : bag-subtract_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs,as:bag(T)]. (bag-subtract(eq;bs;as) ∈ bag(T))
Proof
Definitions occuring in Statement :
bag-subtract: bag-subtract(eq;bs;as),
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-subtract: bag-subtract(eq;bs;as),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
bag-accum_wf,
bag_wf,
bag-drop_wf,
equal_wf,
squash_wf,
true_wf,
bag-drop-commutes,
iff_weakening_equal,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
because_Cache,
hypothesis,
lambdaEquality,
independent_isectElimination,
lambdaFormation,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs,as:bag(T)]. (bag-subtract(eq;bs;as) \mmember{} bag(T))
Date html generated:
2018_05_21-PM-09_49_22
Last ObjectModification:
2017_07_26-PM-06_31_01
Theory : bags_2
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