Nuprl Lemma : pv11_p1_leq_bnum_linorder
∀ldrs_uid:Id ─→ ℤ. (Inj(Id;ℤ;ldrs_uid) ⇒ Linorder(pv11_p1_Ballot_Num();b1,b2.↑(pv11_p1_leq_bnum(ldrs_uid) b1 b2)))
Proof
Definitions occuring in Statement :
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
linorder: Linorder(T;x,y.R[x; y]),
inject: Inj(A;B;f),
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
int: ℤ
Lemmas :
assert_of_bor,
lt_int_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
le_int_wf,
le_weakening,
less_than_wf,
assert_of_lt_int,
iff_transitivity,
assert_wf,
equal-wf-base,
int_subtype_base,
le_wf,
iff_weakening_uiff,
assert_of_band,
assert_of_le_int,
or_wf,
pv11_p1_Ballot_Num_wf,
subtype_base_sq,
decidable__lt,
false_wf,
less-iff-le,
add_functionality_wrt_le,
add-swap,
add-commutes,
le-add-cancel,
le_transitivity,
pv11_p1_leq_bnum_wf,
less_than_transitivity2,
le_weakening2,
less_than_irreflexivity,
less_than_transitivity1,
inject_wf,
Id_wf,
le_antisymmetry,
unit_wf2,
true_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
not-equal-2,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-associates
Latex:
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}
(Inj(Id;\mBbbZ{};ldrs$_{uid}$) {}\mRightarrow{} Linorder(pv11\_p1\_Ballot\_Num();b1,b2.\muparrow{}(pv11\_p1\_leq\_b\000Cnum(ldrs$_{uid}$) b1 b2)))
Date html generated:
2015_07_23-PM-04_44_00
Last ObjectModification:
2015_01_29-AM-11_21_04
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