proposition: Lemma leqtP m (t1 t2 : m.-tuple A) : reflect (forall a b : 'I_m, a <= b -> (tnth t1 a <= tnth t1 b)%O -> (tnth t2 a <= tnth t2 b)%O) (leqt t1 t2).
proof: Proof. apply: (iffP forallP) => [H a b aLb t1aLt1b|H a]. by have /forallP/(_ b) := H a; rewrite aLb t1aLt1b. by apply/forallP=> b; case: leqP => //= aLb; apply/implyP/H. Qed.
imports: mathcomp(all_ssreflect perm algebra.zmodp) mathcomp(zify)