def size_beyond

bendtorch-core@0.1.0.0 · src/tensor/signed_PROOF.bend:420

import Base
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

420# The two branches of a single Inferred size with a nonzero product p: p at
421# most the count divides; p past it leaves an empty input's size 0 and
422# refuses any other.
423def size_beyond(+count: Nat, +extents: List<&2, Signed.Extent>, +rest: Nat, +quotient: Nat,
424  exact: {Nat.mul(quotient, 1n+rest) == count : Nat}, past: {Nat.is_le(1n+rest, count) == False{} : Bool}) ->
425  {Signed.beyond(count, extents) == Done{Signed.filled(extents, U32.from_nat(quotient))} : Result<&2, &2, Signed.Error, List<&2, U32>>}:
426  match quotient:
427    case 0n:
428      %exact : {Signed.beyond(_, extents) == Done{Signed.filled(extents, U32.from_nat(0n))} : Result<&2, &2, Signed.Error, List<&2, U32>>}
429      {==}
430    case 1n+q:
431      Empty.absurd({Signed.beyond(count, extents) == Done{Signed.filled(extents, U32.from_nat(1n+q))} : Result<&2, &2, Signed.Error, List<&2, U32>>},
432        Arith.clash_true(Equal.trans(Bool, True{}, Nat.is_le(1n+rest, count), False{},
433          Equal.trans(Bool, True{}, Nat.is_le(1n+rest, Nat.add(1n+rest, Nat.mul(q, 1n+rest))), Nat.is_le(1n+rest, count),
434            Equal.sym(Bool, Nat.is_le(1n+rest, Nat.add(1n+rest, Nat.mul(q, 1n+rest))), True{}, le_add(1n+rest, Nat.mul(q, 1n+rest))),
435            Equal.cong(Nat, Bool, x => Nat.is_le(1n+rest, x), Nat.add(1n+rest, Nat.mul(q, 1n+rest)), count, exact)),
436          past)))