Nuprl Lemma : pv11_p1_lt_bnum_trans2
∀ldrs_uid:Id ─→ ℤ. ∀b1,b2,b3:pv11_p1_Ballot_Num().
((↑(pv11_p1_leq_bnum(ldrs_uid) b1 b2)) ⇒ (↑(b2 < b3)) ⇒ (↑(b1 < b3)))
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,
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,
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,
less_than_wf,
or_wf,
subtype_base_sq,
decidable__lt,
false_wf,
less-iff-le,
add_functionality_wrt_le,
add-swap,
add-commutes,
le-add-cancel,
less_than_transitivity2,
pv11_p1_lt_bnum_wf,
pv11_p1_leq_bnum_wf,
pv11_p1_Ballot_Num_wf,
Id_wf
Latex:
\mforall{}ldrs$_{uid}$:Id {}\mrightarrow{} \mBbbZ{}. \mforall{}b1,b2,b3:pv11\_p1\_Ballot\_Num().
((\muparrow{}(pv11\_p1\_leq\_bnum(ldrs$_{uid}$) b1 b2)) {}\mRightarrow{} (\muparrow{}(b2 < b3)) {}\mRightarrow{} (\muparrow{}(b1 < b3)))
Date html generated:
2015_07_23-PM-04_43_43
Last ObjectModification:
2015_01_29-AM-11_20_53
Home
Index