mathlib3
c8827532 - chore(algebra/tropical/basic): remove 3 instances (#11920)

Commit
3 years ago
chore(algebra/tropical/basic): remove 3 instances (#11920) The three removed instances are * `covariant_swap_add` (exists since addition is commutative and the non-swapped version is proved); * `covariant_add_lt` (as is, this is a copy of `covariant_add` -- judging from the name, it could have been intended to have a `(<)`, but with `(<)` it is false, see below); * `covariant_swap_add_lt` (exists since addition is commutative and the non-swapped version is proved). Here is a proof that the second instance with `(<)` is false: ```lean lemma not_cov_lt : ¬ covariant_class (tropical ℕ) (tropical ℕ) (+) (<) := begin refine λ h, (lt_irrefl (trop 0) _), cases h, have : trop 0 < trop 1 := show 0 < 1, from zero_lt_one, calc trop 0 = trop 0 + trop 0 : (trop 0).add_self.symm ... < trop 0 + trop 1 : h _ this ... = trop 0 : add_eq_left this.le, end ```
Author
Parents
Loading