SignedPROOF.within_decided: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend as SignedPROOF
Lines 391-403 of bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend&start_line=391&end_line=403

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/tensor/signed.bend as Signed
import bendtorch-core@0.1.0.0/src/tensor/signed_LAWS.bend as Laws

def within_decided(+bound: Nat, +r: Nat, +p: Nat, +within: {Laws.classified(1n+r, Nat.is_le(1n+r, bound)) == Signed.Within{p} : Signed.Product},
  decision: Shape.BoolCase<Nat.is_le(1n+r, bound)>) -> {Nat.is_le(p, bound) == True{} : Bool}:
  match decision:
    case Shape.BTrue{+equal}:
      %Equal.cong(Signed.Product, Nat, within_value, Laws.classified(1n+r, Nat.is_le(1n+r, bound)), Signed.Within{p}, within) :
        {Nat.is_le(_, bound) == True{} : Bool}
      %equal : {Nat.is_le(within_value(Laws.classified(1n+r, _)), bound) == True{} : Bool}
      Equal.sym(Bool, True{}, Nat.is_le(1n+r, bound), equal)
    case Shape.BFalse{equal}:
      Empty.absurd({Nat.is_le(p, bound) == True{} : Bool},
        Arith.clash(Equal.trans(Bool, is_within(Laws.classified(1n+r, False{})), is_within(Laws.classified(1n+r, Nat.is_le(1n+r, bound))), True{},
          Equal.cong(Bool, Bool, x => is_within(Laws.classified(1n+r, x)), False{}, Nat.is_le(1n+r, bound), equal),
          Equal.cong(Signed.Product, Bool, is_within, Laws.classified(1n+r, Nat.is_le(1n+r, bound)), Signed.Within{p}, within))))

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=Empty.absurd
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=BoolCase
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=clash
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/signed.bend&name=Product
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/signed_LAWS.bend&name=classified
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend&name=is_within
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/signed_PROOF.bend&name=within_value