Hint Rewrite @sepcon_emp @emp_sepcon @TT_andp @andp_TT
@exp_sepcon1 @exp_sepcon2
@exp_andp1 @exp_andp2
@sepcon_andp_prop @sepcon_andp_prop'
using (solve [auto with typeclass_instances])
: norm.

Lemma forall_pred_ext  {A}  {NA: NatDed A}: forall B (P Q: B -> A),
(ALL x : B, (P x <--> Q x)) |-- (ALL x : B, P x) <--> (ALL x: B, Q x) .