+
+lemma exteq_canc_sn (A) (B):
+ left_cancellable … (exteq A B).
+/2 width=1 by exteq_repl/ qed-.
+
+lemma exteq_canc_dx (A) (B):
+ right_cancellable … (exteq A B).
+/2 width=1 by exteq_repl/ qed-.
+
+(* Constructions with compose ***********************************************)
+
+lemma compose_repl_fwd_dx (A) (B) (C) (g) (f1) (f2):
+ f1 ≐{A,B} f2 → g ∘ f1 ≐{A,C} g ∘ f2.
+#A #B #C #g #f1 #f2 #Hf12 #a
+whd in ⊢ (??%%); //
+qed.
+
+lemma compose_repl_bak_dx (A) (B) (C) (g) (f1) (f2):
+ f1 ≐{A,B} f2 → g ∘ f2 ≐{A,C} g ∘ f1.
+/3 width=1 by compose_repl_fwd_dx, exteq_sym/
+qed.
+
+lemma compose_repl_fwd_sn (A) (B) (C) (g1) (g2) (f):
+ g1 ≐{B,C} g2 → g1 ∘ f ≐{A,C} g2 ∘ f.
+#A #B #C #g1 #g2 #f #Hg12 #a
+whd in ⊢ (??%%); //
+qed.
+
+lemma compose_repl_bak_sn (A) (B) (C) (g1) (g2) (f):
+ g1 ≐{B,C} g2 → g2 ∘ f ≐{A,C} g1 ∘ f.
+/3 width=1 by compose_repl_fwd_sn, exteq_sym/
+qed.
+
+lemma compose_assoc (A1) (A2) (A3) (A4) (f3:A3→A4) (f2:A2→A3) (f1:A1→A2):
+ f3 ∘ (f2 ∘ f1) ≐ f3 ∘ f2 ∘ f1.
+// qed.