(* *)
(**************************************************************************)
-include "static_2/syntax/ceq_ext_ceq_ext.ma".
+include "static_2/syntax/teq_ext_teq_ext.ma".
include "static_2/relocation/sex_sex.ma".
(* SYNTACTIC EQUIVALENCE FOR SELECTED LOCAL ENVIRONMENTS ********************)
(* Main properties **********************************************************)
-theorem seq_trans: ∀f. Transitive … (seq f).
+theorem seq_trans (f):
+ Transitive … (seq f).
/3 width=5 by sex_trans, ceq_ext_trans/ qed-.
-theorem seq_canc_sn: ∀f. left_cancellable … (seq f).
+theorem seq_canc_sn (f):
+ left_cancellable … (seq f).
/3 width=3 by sex_canc_sn, seq_trans, seq_sym/ qed-.
-theorem seq_canc_dx: ∀f. right_cancellable … (seq f).
+theorem seq_canc_dx (f):
+ right_cancellable … (seq f).
/3 width=3 by sex_canc_dx, seq_trans, seq_sym/ qed-.
-theorem seq_join: ∀f1,L1,L2. L1 ≡[f1] L2 → ∀f2. L1 ≡[f2] L2 →
- ∀f. f1 ⋓ f2 ≘ f → L1 ≡[f] L2.
+theorem seq_join:
+ ∀f1,L1,L2. L1 ≡[f1] L2 → ∀f2. L1 ≡[f2] L2 →
+ ∀f. f1 ⋓ f2 ≘ f → L1 ≡[f] L2.
/2 width=5 by sex_join/ qed-.
-theorem seq_meet: ∀f1,L1,L2. L1 ≡[f1] L2 → ∀f2. L1 ≡[f2] L2 →
- ∀f. f1 ⋒ f2 ≘ f → L1 ≡[f] L2.
+theorem seq_meet:
+ ∀f1,L1,L2. L1 ≡[f1] L2 → ∀f2. L1 ≡[f2] L2 →
+ ∀f. f1 ⋒ f2 ≘ f → L1 ≡[f] L2.
/2 width=5 by sex_meet/ qed-.