PROOF.lin_x: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/PROOF.bend as PROOF
Lines 573-584 of bend-osdev-gf@0.1.1.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&start_line=573&end_line=584

import Base
import bend-osdev-gf@0.1.1.0/gf.bend as G

def lin_x(ts: List<&2, Bool>, vs: List<&2, G.Gf8Bits>, +p: G.Gf8Bits) -> {G.Gf8Bits.x(ss(ts, vs), p) == ss(ts, xl(vs, p)) : G.Gf8Bits}:
  match ts:
    case Nil{}:
      x_zero(p)
    case Con{+t, +tr}:
      match vs:
        case Nil{}:
          x_zero(p)
        case Con{+v, +vr}:
          %lin_x(tr, vr, p) : {G.Gf8Bits.x(G.Gf8Bits.xor(G.Gf8Bits.sel(t, v), ss(tr, vr)), p) == G.Gf8Bits.xor(G.Gf8Bits.sel(t, G.Gf8Bits.x(v, p)), _) : G.Gf8Bits}
          %x_sel(t, v, p) : {G.Gf8Bits.x(G.Gf8Bits.xor(G.Gf8Bits.sel(t, v), ss(tr, vr)), p) == G.Gf8Bits.xor(_, G.Gf8Bits.x(ss(tr, vr), p)) : G.Gf8Bits}
          x_lin(G.Gf8Bits.sel(t, v), ss(tr, vr), p)

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=ss
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=x_lin
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=x_sel
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=x_zero
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/PROOF.bend&name=xl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Bits
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Bits.sel
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Bits.x
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/gf.bend&name=Gf8Bits.xor