(* WEIGHT OF A CLOSURE ******************************************************)
(* activate genv *)
-definition fw: genv → lenv → term → ? ≝ λG,L,T. ♯{L} + ♯{T}.
+definition fw: genv → lenv → term → ? ≝ λG,L,T. ♯❨L❩ + ♯❨T❩.
interpretation "weight (closure)" 'Weight G L T = (fw G L T).
(* Basic properties *********************************************************)
(* Basic_1: was: flt_shift *)
-lemma fw_shift: ∀p,I,G,K,V,T. ♯{G,K.ⓑ{I}V,T} < ♯{G,K,ⓑ{p,I}V.T}.
+lemma fw_shift: ∀p,I,G,K,V,T. ♯❨G,K.ⓑ[I]V,T❩ < ♯❨G,K,ⓑ[p,I]V.T❩.
normalize /2 width=1 by monotonic_le_plus_r/
qed.
-lemma fw_clear: ∀p,I1,I2,G,K,V,T. ♯{G,K.ⓤ{I1},T} < ♯{G,K,ⓑ{p,I2}V.T}.
+lemma fw_clear: ∀p,I1,I2,G,K,V,T. ♯❨G,K.ⓤ[I1],T❩ < ♯❨G,K,ⓑ[p,I2]V.T❩.
normalize /4 width=1 by monotonic_le_plus_r, le_S_S/
qed.
-lemma fw_tpair_sn: ∀I,G,L,V,T. ♯{G,L,V} < ♯{G,L,②{I}V.T}.
+lemma fw_tpair_sn: ∀I,G,L,V,T. ♯❨G,L,V❩ < ♯❨G,L,②[I]V.T❩.
normalize in ⊢ (?→?→?→?→?→?%%); //
qed.
-lemma fw_tpair_dx: ∀I,G,L,V,T. ♯{G,L,T} < ♯{G,L,②{I}V.T}.
+lemma fw_tpair_dx: ∀I,G,L,V,T. ♯❨G,L,T❩ < ♯❨G,L,②[I]V.T❩.
normalize in ⊢ (?→?→?→?→?→?%%); //
qed.
-lemma fw_lpair_sn: ∀I,G,L,V,T. ♯{G,L,V} < ♯{G,L.ⓑ{I}V,T}.
+lemma fw_lpair_sn: ∀I,G,L,V,T. ♯❨G,L,V❩ < ♯❨G,L.ⓑ[I]V,T❩.
normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
qed.