proposition: Lemma int_abs_nonpos x : x ≤ 0 → f (int_abs Z N x) = -x.
proof: Proof. intros E. rewrite <-int_abs_negate, int_abs_nonneg; intuition. now apply flip_nonpos_negate. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.naturals MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.nat_int MathClasses.theory.integers MathClasses.theory.rings MathClasses.orders.rings