Definition rtacP := sigT (fun tac: rtac typ (expr typ func) =>
  forall tbl: SymEnv.functions RType_typ, rtac_sound (Expr_expr := func_defs.Expr_expr_fs tbl) tac).(************************************************

Rtac Part

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Definition my_lemma := lemma typ (ExprCore.expr typ func) (ExprCore.expr typ func).Definition THEN' (r1 r2 : rtac typ (expr typ func)) := THEN r1 (runOnGoals r2).Definition THEN (r1 r2 : rtac typ (expr typ func)) :=
  THEN' r1 (THEN' (INSTANTIATE typ func) r2).Instance MentionsAnyOk : MentionsAnyOk MA _ _.

Lemma THEN_sound : forall t1 t2, rtac_sound (Expr_expr := func_defs.Expr_expr_fs tbl) t1 -> rtac_sound (Expr_expr := func_defs.Expr_expr_fs tbl) t2 -> rtac_sound (Expr_expr := func_defs.Expr_expr_fs tbl) (THEN t1 t2).