Nuprl Lemma : ranked-eo_wf
∀[Info:Type]. ∀[L:Id ─→ (Info List)]. ∀[rk:(i:Id × ℕ||L i||) ─→ ℕ].
ranked-eo(L;rk) ∈ EO+(Info) supposing ∀i:Id. ∀j:ℕ||L i||. ∀k:ℕj. rk <i, k> < rk <i, j>
Proof
Definitions occuring in Statement :
ranked-eo: ranked-eo(L;rk),
event-ordering+: EO+(Info),
Id: Id,
length: ||as||,
list: T List,
int_seg: {i..j-},
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
apply: f a,
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
natural_number: $n,
universe: Type
Lemmas :
mk-extended-eo_wf,
btrue_wf,
less_than_wf,
int_seg_wf,
length_wf,
lt_int_wf,
subtract_wf,
zero-le-nat,
non_neg_length,
length_wf_nat,
le_wf,
lelt_wf,
select_wf,
int_seg_subtype-nat,
false_wf,
squash_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
not_squash,
less_than_transitivity2,
le_weakening2,
assert_of_lt_int,
assert_wf,
not_wf,
assert_witness,
all_wf,
Id_wf,
nat_wf,
list_wf,
less_than_irreflexivity,
decidable__le,
not-le-2,
not-equal-2,
sq_stable__le,
add_functionality_wrt_le,
zero-add,
add-zero,
le-add-cancel,
condition-implies-le,
minus-one-mul,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
minus-zero,
decidable__lt,
less-iff-le,
le-add-cancel2,
subtract-is-less,
atom2_subtype_base,
decidable__equal_int,
int_subtype_base,
true_wf,
iff_weakening_equal,
le_weakening,
less_than_transitivity1
Latex:
\mforall{}[Info:Type]. \mforall{}[L:Id {}\mrightarrow{} (Info List)]. \mforall{}[rk:(i:Id \mtimes{} \mBbbN{}||L i||) {}\mrightarrow{} \mBbbN{}].
ranked-eo(L;rk) \mmember{} EO+(Info) supposing \mforall{}i:Id. \mforall{}j:\mBbbN{}||L i||. \mforall{}k:\mBbbN{}j. rk <i, k> < rk <i, j>
Date html generated:
2015_07_21-PM-04_42_02
Last ObjectModification:
2015_02_04-PM-05_58_22
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