interpretation "extensional equivalence (nstream)"
'ExtEq A t1 t2 = (eq_stream A t1 t2).
+definition eq_stream_repl (A) (R:relation …) ≝
+ ∀t1,t2. t1 ≐⦋A⦌ t2 → R t1 t2.
+
definition eq_stream_repl_back (A) (R:predicate …) ≝
- ∀t1,t2. t1 ≐⦋A⦌ t2 → R t1 → R t2.
+ ∀t1. R t1 → ∀t2. t1 ≐⦋A⦌ t2 → R t2.
definition eq_stream_repl_fwd (A) (R:predicate …) ≝
- ∀t1,t2. t2 ≐⦋A⦌ t1 → R t1 → R t2.
+ ∀t1. R t1 → ∀t2. t2 ≐⦋A⦌ t1 → R t2.
(* Basic inversion lemmas ***************************************************)