Nuprl Lemma : not-pv11_p1_leq_bnum
∀ldrs_uid:Id ─→ ℤ. ∀b,b':pv11_p1_Ballot_Num().
(Inj(Id;ℤ;ldrs_uid) ⇒ (¬↑(pv11_p1_leq_bnum(ldrs_uid) b b')) ⇒ (↑(b' < b)))
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],
not: ¬A,
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
int: ℤ
Lemmas :
pv11_p1_leq_bnum_linorder,
not_wf,
assert_wf,
pv11_p1_leq_bnum_wf,
inject_wf,
Id_wf,
pv11_p1_Ballot_Num_wf,
pv11_p1_leq_bnum_implies_eq_or_lt,
assert_elim,
and_wf,
equal_wf,
subtype_base_sq,
union_subtype_base,
unit_wf2,
product_subtype_base,
int_subtype_base,
atom2_subtype_base,
unit_subtype_base,
not_assert_elim,
btrue_neq_bfalse
Latex:
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}b,b':pv11\_p1\_Ballot\_Num().
(Inj(Id;\mBbbZ{};ldrs$_{uid}$) {}\mRightarrow{} (\mneg{}\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}\mbackslash{}ff\000C24) b b')) {}\mRightarrow{} (\muparrow{}(b' < b)))
Date html generated:
2015_07_23-PM-04_44_03
Last ObjectModification:
2015_01_29-AM-11_20_18
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