diff --git a/library/theories/move.lean b/library/theories/move.lean index 2e6fa1bf0..bfd2c5687 100644 --- a/library/theories/move.lean +++ b/library/theories/move.lean @@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE. Temporary file; move in Lean3. -/ -import data.set algebra.order_bigops +import data.set algebra.order_bigops algebra.ordered_field import data.finset data.list.sort import data.real @@ -39,6 +39,12 @@ calc b < c - a : lt_sub_left_of_add_lt H ... ≤ c : sub_le_self _ Hb + theorem lt_mul_of_div_lt_of_pos {A : Type} {a b c : A} [linear_ordered_field A] + (Hc : c > 0) (H : a / c < b) : a < b * c := + calc + a = a / c * c : !div_mul_cancel (ne.symm (ne_of_lt Hc)) + ... < b * c : mul_lt_mul_of_pos_right H Hc + -- move to init.quotient namespace quot