Nuprl Lemma : imax-bag-lb
∀[bs:bag(ℤ)]. (0 < #(bs) ⇒ imax-bag(bs) ↓∈ bs)
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
imax-bag: imax-bag(bs),
bag-size: #(bs),
bag: bag(T),
less_than: a < b,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
squash: ↓T,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
so_apply: x[s],
all: ∀x:A. B[x],
sq_stable: SqStable(P),
bag-member: x ↓∈ bs,
exists: ∃x:A. B[x],
imax-bag: imax-bag(bs),
bag-size: #(bs),
and: P ∧ Q,
cand: A c∧ B,
nat: ℕ
Lemmas referenced :
bag_to_squash_list,
sq_stable__all,
less_than_wf,
bag-size_wf,
bag-member_wf,
imax-bag_wf,
sq_stable__bag-member,
squash_wf,
imax-list-member,
equal-wf-base,
bag_wf,
list_subtype_base,
int_subtype_base,
l_member_wf,
imax-list_wf,
length_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
intEquality,
hypothesisEquality,
imageElimination,
natural_numberEquality,
hypothesis,
applyEquality,
because_Cache,
sqequalRule,
lambdaEquality,
independent_isectElimination,
independent_functionElimination,
dependent_functionElimination,
imageMemberEquality,
baseClosed,
productElimination,
promote_hyp,
rename,
dependent_pairFormation,
independent_pairFormation,
productEquality,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
functionEquality,
setElimination
Latex:
\mforall{}[bs:bag(\mBbbZ{})]. (0 < \#(bs) {}\mRightarrow{} imax-bag(bs) \mdownarrow{}\mmember{} bs)
Date html generated:
2016_10_25-AM-10_32_15
Last ObjectModification:
2016_07_12-AM-06_47_50
Theory : bags
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