{P : Type} {a b c : P} {ab : a = b} {ac : a = c} {bc : b = c} (abc : ab @ bc = ac) {ab' : a = b} {ac' : a = c} {bc' : b = c} (abc' : ab' @ bc' = ac') (k12 : ab = ab') (k13 : ac = ac') (k23 : bc = bc') (k123 : prism' abc abc' k12 k13 k23) : prism abc abc' (equiv_p1_1q k12) (equiv_p1_1q k13) (equiv_p1_1q k23). Proof. induction ab. induction bc. induction abc. induction k12. induction k23. induction k13. unfold prism' in k123. induction (moveR_Vp _ _ _ k123); clear k123. simpl. reflexivity. Defined.
Require Import Basics Types.Paths WildCat Join.Core HoTT.Tactics.