Nuprl Lemma : imax-bag-ub
∀[bs:bag(ℤ)]. ∀[x:ℤ]. (x ↓∈ bs ⇒ (x ≤ imax-bag(bs)))
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
imax-bag: imax-bag(bs),
bag: bag(T),
uall: ∀[x:A]. B[x],
le: A ≤ B,
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
sq_stable: SqStable(P),
le: A ≤ B,
not: ¬A,
false: False,
imax-bag: imax-bag(bs),
bag-size: #(bs),
subtype_rel: A ⊆r B,
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top
Lemmas referenced :
bag_to_squash_list,
sq_stable__all,
bag-member_wf,
le_wf,
imax-bag_wf,
bag-size-bag-member,
sq_stable__le,
less_than'_wf,
squash_wf,
imax-list-ub,
bag_wf,
list-subtype-bag,
subtype_rel_self,
l_exists_iff,
l_member_wf,
bag-member-list,
decidable__int_equal,
decidable__le,
satisfiable-full-omega-tt,
intformnot_wf,
intformle_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
hypothesisEquality,
imageElimination,
intEquality,
hypothesis,
sqequalRule,
lambdaEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
dependent_pairFormation,
imageMemberEquality,
baseClosed,
dependent_functionElimination,
independent_pairEquality,
voidElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
rename,
hyp_replacement,
Error :applyLambdaEquality,
functionEquality,
isect_memberEquality,
applyEquality,
setElimination,
setEquality,
independent_pairFormation,
unionElimination,
natural_numberEquality,
int_eqEquality,
voidEquality,
computeAll,
productEquality
Latex:
\mforall{}[bs:bag(\mBbbZ{})]. \mforall{}[x:\mBbbZ{}]. (x \mdownarrow{}\mmember{} bs {}\mRightarrow{} (x \mleq{} imax-bag(bs)))
Date html generated:
2016_10_25-AM-10_32_11
Last ObjectModification:
2016_07_12-AM-06_48_04
Theory : bags
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