Nuprl Lemma : pv11_p1_leq_bnum_implies_eq_or_lt
∀ldrs_uid:Id ─→ ℤ. ∀b1,b2:pv11_p1_Ballot_Num().
(Inj(Id;ℤ;ldrs_uid) ⇒ (↑(pv11_p1_leq_bnum(ldrs_uid) b1 b2)) ⇒ ((b1 = b2 ∈ pv11_p1_Ballot_Num()) ∨ (↑(b1 < b2))))
Proof
Definitions occuring in Statement :
pv11_p1_lt_bnum: pv11_p1_lt_bnum(ldrs_uid),
pv11_p1_leq_bnum: pv11_p1_leq_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
inject: Inj(A;B;f),
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
apply: f a,
function: x:A ─→ B[x],
int: ℤ,
equal: s = t ∈ T
Lemmas :
assert_wf,
pv11_p1_leq_bnum_wf,
inject_wf,
Id_wf,
unit_wf2,
bor_wf,
lt_int_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
le_int_wf,
or_wf,
less_than_wf,
equal-wf-base,
int_subtype_base,
le_wf,
equal_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bor,
assert_of_lt_int,
assert_of_band,
assert_of_le_int,
decidable__lt,
false_wf,
less-iff-le,
add_functionality_wrt_le,
add-swap,
add-commutes,
le-add-cancel,
decidable__equal_int,
not-equal-2,
add-associates,
equal-unit
Latex:
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}b1,b2:pv11\_p1\_Ballot\_Num().
(Inj(Id;\mBbbZ{};ldrs$_{uid}$) {}\mRightarrow{} (\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}\mbackslash{}ff2\000C4) b1 b2)) {}\mRightarrow{} ((b1 = b2) \mvee{} (\muparrow{}(b1 < b2))))
Date html generated:
2015_07_23-PM-04_43_58
Last ObjectModification:
2015_01_29-AM-11_21_02
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