Nuprl Lemma : the-member-bag-rep
∀[T:Type]. ∀[n:ℕ]. ∀[a:T]. a ↓∈ bag-rep(n;a) supposing 0 < n
Proof
Definitions occuring in Statement :
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
universe: Type,
bag-member: x ↓∈ bs,
bag-rep: bag-rep(n;x)
Lemmas :
primrec-unroll,
less_than_wf,
nat_wf,
equal-wf-T-base,
assert_wf,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity,
bnot_wf,
not_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
primrec_wf,
bag_wf,
decidable__le,
subtract_wf,
false_wf,
not-le-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
le_wf,
empty-bag_wf,
cons-bag_wf,
int_seg_wf,
bag-member_wf,
bag-member-cons
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[a:T]. a \mdownarrow{}\mmember{} bag-rep(n;a) supposing 0 < n
Date html generated:
2015_07_23-AM-11_25_29
Last ObjectModification:
2015_01_28-PM-11_16_10
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