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15 include "delayed_updating/substitution/lift.ma".
16 include "delayed_updating/syntax/path_depth.ma".
17 include "ground/relocation/tr_pushs.ma".
19 (* LIFT FOR PATH ***********************************************************)
21 (* Basic constructions with depth ******************************************)
24 (⫯*[❘p❘]f) ∘ (↑[p]𝐢) = ↑[p]f.
26 [ #f <lift_rmap_empty <lift_rmap_empty <tr_pushs_zero
27 | * [ #n ] #p #IH #f //
28 <lift_rmap_d_sn <lift_rmap_d_sn <depth_d_sn
29 @(trans_eq … (IH …)) -IH