GatherPROOF.counted_is: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend as GatherPROOF
Lines 119-127 of bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend&start_line=119&end_line=127

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/gather.bend as Gather
import bendtorch-core@0.1.0.0/src/tensor/gather_LAWS.bend as Laws

# The entry count rewrites to its value.
def counted_is(+entries: List<&2, U32>, +index: Shape.Shape, +value: Bool,
  given: {Nat.is_eq(Laws.length(entries), Shape.elements(index)) == value : Bool}) ->
  {value == Nat.is_eq(Gather.count(entries), Shape.elements(index)) : Bool}:
  Equal.sym(Bool, Nat.is_eq(Gather.count(entries), Shape.elements(index)), value,
    Equal.trans(Bool, Nat.is_eq(Gather.count(entries), Shape.elements(index)), Nat.is_eq(Laws.length(entries), Shape.elements(index)),
      value,
      Equal.cong(Nat, Bool, n => Nat.is_eq(n, Shape.elements(index)), Gather.count(entries), Laws.length(entries), count_length(entries)),
      given))

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  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=U32
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=elements
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=count
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_LAWS.bend&name=length
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend&name=count_length