Nuprl Lemma : pv11_p1_leq_bnum_implies_eq
∀ldrs_uid:Id ─→ ℤ. ∀b,b':pv11_p1_Ballot_Num().
(Inj(Id;ℤ;ldrs_uid)
⇒ (↑(pv11_p1_leq_bnum(ldrs_uid) b b'))
⇒ (↑(pv11_p1_leq_bnum(ldrs_uid) b' b))
⇒ (b = b' ∈ pv11_p1_Ballot_Num()))
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,
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,
equal: s = t ∈ T
Lemmas :
unit_wf2,
equal-unit,
Id_wf,
assert_wf,
pv11_p1_leq_bnum_wf,
inject_wf,
pv11_p1_Ballot_Num_wf,
iff_transitivity,
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,
iff_weakening_uiff,
assert_of_bor,
assert_of_lt_int,
assert_of_band,
assert_of_le_int,
less_than_transitivity2,
le_weakening2,
less_than_irreflexivity,
less_than_transitivity1,
le_weakening,
le_antisymmetry
Latex:
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}b,b':pv11\_p1\_Ballot\_Num().
(Inj(Id;\mBbbZ{};ldrs$_{uid}$)
{}\mRightarrow{} (\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}$) b b'))
{}\mRightarrow{} (\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}$) b' b))
{}\mRightarrow{} (b = b'))
Date html generated:
2015_07_23-PM-04_43_55
Last ObjectModification:
2015_01_29-AM-11_20_43
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