Nuprl Lemma : first-choosable-property
∀[M:Type ─→ Type]. ∀[r:pRunType(P.M[P])]. ∀[t:ℕ+]. ∀[n:ℕ].
first-choosable(r;t) ≤ n supposing ↑lg-is-source(run-intransit(r;t);n)
Proof
Definitions occuring in Statement :
first-choosable: first-choosable(r;t),
run-intransit: run-intransit(r;t),
pRunType: pRunType(T.M[T]),
lg-is-source: lg-is-source(g;i),
nat_plus: ℕ+,
nat: ℕ,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
function: x:A ─→ B[x],
universe: Type
Lemmas :
sq_stable__le,
run-intransit_wf,
ldag_wf,
pInTransit_wf,
lt_int_wf,
search_wf,
lg-size_wf,
lg-is-source_wf,
int_seg_subtype-nat,
nat_wf,
false_wf,
int_seg_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
subtract_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
assert_wf,
nat_plus_wf,
pRunType_wf,
search_property,
decidable__le,
lelt_wf,
decidable__lt,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
add-commutes,
not-le-2,
add-associates,
add_functionality_wrt_le,
zero-add,
le-add-cancel-alt,
assert_elim,
not_assert_elim,
and_wf,
btrue_neq_bfalse,
add-zero,
le-add-cancel
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]. \mforall{}[r:pRunType(P.M[P])]. \mforall{}[t:\mBbbN{}\msupplus{}]. \mforall{}[n:\mBbbN{}].
first-choosable(r;t) \mleq{} n supposing \muparrow{}lg-is-source(run-intransit(r;t);n)
Date html generated:
2015_07_23-AM-11_16_59
Last ObjectModification:
2015_01_28-PM-11_19_44
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