def times_within

bendtorch-core@0.1.0.0 · src/tensor/signed_PROOF.bend:330

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
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

330def times_within(+bound: Nat, +less: Nat, +rest: Nat, decision: Shape.BoolCase<Nat.is_le(1n+rest, bound)>) ->
331  {Signed.times(bound, 1n+less, Laws.classified(1n+rest, Nat.is_le(1n+rest, bound))) == Laws.classify(bound, Nat.mul(1n+less, 1n+rest)) : Signed.Product}:
332  match decision:
333    case Shape.BTrue{equal}:
334      %equal : {Signed.times(bound, 1n+less, Laws.classified(1n+rest, _)) == Laws.classify(bound, Nat.mul(1n+less, 1n+rest)) : Signed.Product}
335      times_scaled(bound, less, rest, Shape.bool_case(Nat.is_lt(bound, 1n+less)))
336    case Shape.BFalse{+equal}:
337      %equal : {Signed.times(bound, 1n+less, Laws.classified(1n+rest, _)) == Laws.classify(bound, Nat.mul(1n+less, 1n+rest)) : Signed.Product}
338      %Equal.sym(Bool, Nat.is_le(Nat.mul(1n+less, 1n+rest), bound), False{},
339        not_le_add(1n+rest, Nat.mul(less, 1n+rest), bound, Equal.sym(Bool, False{}, Nat.is_le(1n+rest, bound), equal))) :
340        {Signed.Beyond{} == Laws.classified(Nat.mul(1n+less, 1n+rest), _) : Signed.Product}
341      {==}