-definition ifr (p) (q): relation2 prototerm prototerm ≝
- λt1,t2. ∃k:pnat.
- let r ≝ p●𝗔◗𝗟◗q in
- ∧∧ 𝗟◗q = ↳[k](𝗟◗q) & r◖𝗱k ϵ t1 &
- t1[⋔r←↑[𝐮❨k❩](t1⋔(p◖𝗦))] ⇔ t2
+(**) (* explicit ninj because we cannot declare the expectd type of k *)
+definition ifr (r): relation2 prototerm prototerm ≝
+ λt1,t2.
+ ∃∃p,q,k. p●𝗔◗𝗟◗q = r &
+ (𝗟◗q) = ↳[ninj k](𝗟◗q) & r◖𝗱k ϵ t1 &
+ t1[⋔r←↑[𝐮❨ninj k❩](t1⋔(p◖𝗦))] ⇔ t2