Set: pp::colors Notation 10 if _ then _ : implies if ⊤ then ⊥ if ⊤ then (if a then ⊥) implies ⊤ (implies a ⊥) Notation 100 _ |- _ ; _ : f f c d e c |- d ; e (c !) ! fact (fact c) [ c ; d ] [ c ; ([ d ; e ]) ] g c (g d e) Notation 40 _ << _ end : h d << e end [ c ; d << e end ] g c (h d e) c ** d ++ e ** c p1 ∨ p2 ∧ p3 r (s c d) (s e c) or p1 (and p2 p3) c = d ∨ d = c ¬ p1 ∨ p2 p1 ∧ p3 ∨ p2 ∧ p3 or (not p1) p2 or (and p1 p3) (and p2 p3)