normalize //
qed.
-lemma tw_shift: ∀L,T. ♯{L, T} ≤ ♯{L @@ T}.
-#L elim L //
-#K #I #V #IHL #T
-@transitive_le [3: @IHL |2: /2 width=2/ | skip ]
-qed.
-
lemma fw_tpair_sn: ∀I,L,V,T. ♯{L, V} < ♯{L, ②{I}V.T}.
normalize in ⊢ (?→?→?→?→?%%); //
qed.
normalize in ⊢ (?→?→?→?→?%%); //
qed.
-lemma fw_tpair_dx_sn: ∀I1,I2,L,V1,V2,T. ♯{L, V2} < ♯{L, ②{I1}V1.②{I2}V2.T}.
-normalize in ⊢ (?→?→?→?→?→?→?%%); /2 width=1 by monotonic_le_plus_r/ (**) (* auto too slow without trace *)
-qed.
-
-lemma fw_tpair_sn_sn_shift: ∀I,I1,I2,L,V1,V2,T.
- ♯{L.ⓑ{I}V1, T} < ♯{L, ②{I1}V1.②{I2}V2.T}.
-normalize in ⊢ (?→?→?→?→?→?→?→?%%); /3 width=1/
-qed.
-
-lemma fw_tpair_sn_dx_shift: ∀I,I1,I2,L,V1,V2,T.
- ♯{L.ⓑ{I}V2, T} < ♯{L, ②{I1}V1.②{I2}V2.T}.
-normalize in ⊢ (?→?→?→?→?→?→?→?%%); /2 width=1 by monotonic_le_plus_r/ (**) (* auto too slow without trace *)
-qed.
-
lemma fw_lpair_sn: ∀I,L,V,T. ♯{L, V} < ♯{L.ⓑ{I}V, T}.
normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/ (**) (* auto too slow without trace *)
qed.
(* Basic_1: removed theorems 7:
- flt_thead_sx flt_thead_dx flt_arith0 flt_arith1 flt_arith2 flt_trans
- flt_wf_ind
+ flt_thead_sx flt_thead_dx flt_trans
+ flt_arith0 flt_arith1 flt_arith2 flt_wf_ind
*)
(* Basic_1: removed local theorems 1: q_ind *)