def within_decided

bendtorch-core@0.1.0.0 · src/tensor/signed_PROOF.bend:391

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

391def within_decided(+bound: Nat, +r: Nat, +p: Nat, +within: {Laws.classified(1n+r, Nat.is_le(1n+r, bound)) == Signed.Within{p} : Signed.Product},
392  decision: Shape.BoolCase<Nat.is_le(1n+r, bound)>) -> {Nat.is_le(p, bound) == True{} : Bool}:
393  match decision:
394    case Shape.BTrue{+equal}:
395      %Equal.cong(Signed.Product, Nat, within_value, Laws.classified(1n+r, Nat.is_le(1n+r, bound)), Signed.Within{p}, within) :
396        {Nat.is_le(_, bound) == True{} : Bool}
397      %equal : {Nat.is_le(within_value(Laws.classified(1n+r, _)), bound) == True{} : Bool}
398      Equal.sym(Bool, True{}, Nat.is_le(1n+r, bound), equal)
399    case Shape.BFalse{equal}:
400      Empty.absurd({Nat.is_le(p, bound) == True{} : Bool},
401        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{},
402          Equal.cong(Bool, Bool, x => is_within(Laws.classified(1n+r, x)), False{}, Nat.is_le(1n+r, bound), equal),
403          Equal.cong(Signed.Product, Bool, is_within, Laws.classified(1n+r, Nat.is_le(1n+r, bound)), Signed.Within{p}, within))))