ProofCells.memn_range.cases: def of minebender-game@1.0.0.0
Import: import minebender-game@1.0.0.0/proof_cells.bend as ProofCells
Lines 131-141 of minebender-game@1.0.0.0/proof_cells.bend: https://jend.leeeet.dev/read.txt?path=minebender-game@1.0.0.0/proof_cells.bend&start_line=131&end_line=141

import Base
import minebender-game@1.0.0.0/proof_base.bend as P

def memn_range.cases(+p: Nat, +i: Nat, r: Or({Nat.is_lt(i, p) == True{} : Bool}, {i == p : Nat}),
  ih: {Nat.is_lt(i, p) == True{} : Bool} -> {memn(List.range(p), i) == True{} : Bool}) ->
  {memn(List.append(&2, Nat, List.range(p), [p]), i) == True{} : Bool}:
  match r:
    case Inl{lt}:
      memn_append_l(List.range(p), [p], i, ih(lt))
    case Inr{eq}:
      memn_append_r(List.range(p), [p], i,
        %Equal.sym(Nat, i, p, eq) : {Bool.or(Nat.is_eq(p, _), False{}) == True{} : Bool};
        %Equal.sym(Bool, Nat.is_eq(p, p), True{}, P.eq_refl(p)) : {Bool.or(_, False{}) == True{} : Bool};
        {==})

Uses (15):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.or
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Either
  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=List.range
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Or
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_base.bend&name=eq_refl
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_cells.bend&name=memn
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_cells.bend&name=memn_append_l
  https://jend.leeeet.dev/definition.txt?path=minebender-game@1.0.0.0/proof_cells.bend&name=memn_append_r