Nuprl Lemma : pv11_p1_lt_bnum_implies_not2
∀ldrs_uid:Id ─→ ℤ. ∀b1,b2:pv11_p1_Ballot_Num(). ((↑(b1 < b2)) ⇒ (↑(b2 < b1)) ⇒ False)
Proof
Definitions occuring in Statement :
pv11_p1_lt_bnum: pv11_p1_lt_bnum(ldrs_uid),
pv11_p1_Ballot_Num: pv11_p1_Ballot_Num(),
Id: Id,
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
false: False,
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,
assert_of_lt_int,
iff_transitivity,
assert_wf,
equal-wf-base,
int_subtype_base,
less_than_wf,
iff_weakening_uiff,
assert_of_band,
or_wf,
less_than_transitivity2,
le_weakening2,
less_than_irreflexivity,
less_than_transitivity1,
le_weakening,
pv11_p1_lt_bnum_wf,
pv11_p1_Ballot_Num_wf,
Id_wf
Latex:
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}b1,b2:pv11\_p1\_Ballot\_Num(). ((\muparrow{}(b1 < b2)) {}\mRightarrow{} (\muparrow{}(b2 < \000Cb1)) {}\mRightarrow{} False)
Date html generated:
2015_07_23-PM-04_43_50
Last ObjectModification:
2015_01_29-AM-11_20_35
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