ProofGen.firsts_append: law of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_gen.bend as ProofGen
Lines 630-634 of minebender-game@1.0.0.0/proof_gen.bend: https://jend.leeeet.dev/read.txt?path=minebender-game@1.0.0.0/proof_gen.bend&start_line=630&end_line=634

import Base
import minebender-game@1.0.0.0/types.bend as T
import minebender-game@1.0.0.0/game.bend as G

law firsts_append:
  for +z: G.Zone
  for +xs: List<&2, T.Pos>
  for +ys: List<&2, T.Pos>
  {outs(z, List.append(&2, T.Pos, xs, ys)) == Nat.add(outs(z, xs), outs(z, ys)) : Nat}

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.pick
  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=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/game.bend&name=Zone
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/game.bend&name=gen.out
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_base.bend&name=add_assoc
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_gen.bend&name=outs
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/types.bend&name=Pos