Nuprl Lemma : imax-bag_wf
∀[bs:bag(ℤ)]. imax-bag(bs) ∈ ℤ supposing 0 < #(bs)
Proof
Definitions occuring in Statement :
imax-bag: imax-bag(bs),
bag-size: #(bs),
bag: bag(T),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
bag: bag(T),
all: ∀x:A. B[x],
prop: ℙ,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
imax-bag: imax-bag(bs),
bag-size: #(bs),
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
nat: ℕ,
implies: P ⇒ Q,
guard: {T},
set-equal: set-equal(T;x;y)
Lemmas referenced :
member-permutation,
bag_wf,
nat_wf,
bag-size_wf,
less_than_wf,
imax-list_functionality,
true_wf,
squash_wf,
member_wf,
equal-wf-base,
imax-list_wf,
permutation_weakening,
permutation_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lemma_by_obid,
isectElimination,
thin,
intEquality,
hypothesis,
promote_hyp,
lambdaFormation,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
because_Cache,
independent_isectElimination,
pointwiseFunctionality,
sqequalRule,
pertypeElimination,
productElimination,
productEquality,
applyEquality,
lambdaEquality,
imageElimination,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
axiomEquality,
setElimination,
rename,
isect_memberEquality,
independent_functionElimination
Latex:
\mforall{}[bs:bag(\mBbbZ{})]. imax-bag(bs) \mmember{} \mBbbZ{} supposing 0 < \#(bs)
Date html generated:
2016_05_15-PM-02_30_47
Last ObjectModification:
2016_01_16-AM-08_54_13
Theory : bags
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