Perm.internal_trans_eq: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/perm.bend as Perm
Lines 39-42 of bend-mathlib@0.8.1.0/perm.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/perm.bend&start_line=39&end_line=42

import Base
import bendlib-kernel-list@1.0.0.0/list.bend as K

def internal_trans_eq(-A: Data, +s1: List<&2, Nat>, +s2: List<&2, Nat>, +xs: List<&2, A>, -ys: List<&2, A>, -zs: List<&2, A>, e1: K.perm_steps(A, s1, xs, ys), e2: K.perm_steps(A, s2, ys, zs)) -> K.perm_steps(A, List.append(&2, Nat, s1, s2), xs, zs):
  %Equal.sym(List<&2, A>, K.apply(A, List.append(&2, Nat, s1, s2), xs), K.apply(A, s2, K.apply(A, s1, xs)), internal_apply_app(A, s1, s2, xs)) : {_ == zs : List<&2, A>}
  %Equal.sym(List<&2, A>, K.apply(A, s1, xs), ys, e1) : {K.apply(A, s2, _) == zs : List<&2, A>}
  e2

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/perm.bend&name=internal_apply_app
  https://jend.leeeet.dev/definition.txt?path=bendlib-kernel-list@1.0.0.0/list.bend&name=apply
  https://jend.leeeet.dev/definition.txt?path=bendlib-kernel-list@1.0.0.0/list.bend&name=perm_steps