nth'_seq'@{} (n i : nat) (H : (i < length (seq' n))%nat) : (nth' (seq' n) i H).1 = i. Proof. unshelve lhs_V nrapply nth'_list_map. 1: by rewrite length_list_map. unshelve lhs nrapply (ap011D (fun x y => nth' x _ y) _ idpath). 2: apply seq_seq'. apply isinj_some. lhs_V nrapply nth_nth'. apply nth_seq. by rewrite length_seq' in H. Defined.
Require Import Basics.Overture Basics.Tactics Basics.PathGroupoids Basics.Trunc Require Import Types.Paths Types.Unit Types.Prod Types.Sigma Types.Sum