Nuprl Lemma : first-choosable_wf
∀[M:Type ─→ Type]. ∀[t:ℕ+]. ∀[r:ℕt ─→ (ℤ × Id × Id × pMsg(P.M[P])? × System(P.M[P]))]. (first-choosable(r;t) ∈ ℕ)
Proof
Definitions occuring in Statement :
first-choosable: first-choosable(r;t),
System: System(P.M[P]),
pMsg: pMsg(P.M[P]),
Id: Id,
nat_plus: ℕ+,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
so_apply: x[s],
unit: Unit,
member: t ∈ T,
function: x:A ─→ B[x],
product: x:A × B[x],
union: left + right,
natural_number: $n,
int: ℤ,
universe: Type
Lemmas :
int_seg_wf,
Id_wf,
pMsg_wf,
unit_wf2,
System_wf,
nat_plus_wf,
labeled-graph_wf,
pInTransit_wf,
subtract_wf,
decidable__le,
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,
subtract-is-less,
lelt_wf,
lt_int_wf,
search_wf,
lg-size_wf,
lg-is-source_wf,
int_seg_subtype-nat,
nat_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
le_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[r:\mBbbN{}t {}\mrightarrow{} (\mBbbZ{} \mtimes{} Id \mtimes{} Id \mtimes{} pMsg(P.M[P])? \mtimes{} System(P.M[P]))].
(first-choosable(r;t) \mmember{} \mBbbN{})
Date html generated:
2015_07_23-AM-11_16_55
Last ObjectModification:
2015_01_28-PM-11_18_36
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