def below

bendtorch-core@0.1.0.0 · src/tensor/permute_build_proof.bend:600

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/model.bend as Model
import bendtorch-core@0.1.0.0/src/tensor/contracts/build_facts.bend as Facts
import bendtorch-core@0.1.0.0/src/shape/index_proofs.bend as Index
import bendtorch-core@0.1.0.0/src/storage/LAWS.bend as StorageLaws
import bendtorch-core@0.1.0.0/src/storage/api.bend as Api

600# A subtree whose positions all lie below k is the same for k and 1 + k.
601def below(+input: Shape.Shape, +axes: List<&2, U32>, +fill: F32, +ops: List<&2, StorageLaws.Op>, +k: Nat, +depth: Nat, +b: Nat, +h: {Nat.is_le(Nat.add(Model.capacity(depth), b), k) == True{} : Bool}) ->
602  {spec(input, axes, fill, ops, k, depth, b) == spec(input, axes, fill, ops, 1n+k, depth, b) : Array<F32>}:
603  match depth:
604    case 0n:
605      +lower = Facts.below_true(b, k, h)
606      %Equal.sym(Bool, Nat.is_lt(b, k), True{}, lower) :
607        {ALeaf{leaf(input, axes, fill, ops, b, _)} == ALeaf{leaf(input, axes, fill, ops, b, Nat.is_lt(b, 1n+k))} : Array<F32>}
608      %Equal.sym(Bool, Nat.is_lt(b, 1n+k), True{}, Facts.lt_succ_right(b, k, lower)) :
609        {ALeaf{word(input, axes, fill, ops, b)} == ALeaf{leaf(input, axes, fill, ops, b, _)} : Array<F32>}
610      {==}
611    case 1n+inner:
612      +c = Model.capacity(inner)
613      +high = Nat.add(c, b)
614      +nested = Equal.trans(Bool, Nat.is_le(Nat.add(c, high), k), Nat.is_le(Nat.add(Nat.add(c, c), b), k), True{},
615        Equal.cong(Nat, Bool, x => Nat.is_le(x, k), Nat.add(c, high), Nat.add(Nat.add(c, c), b), Index.add_assoc(c, c, b)), h)
616      +low_h = Facts.le_trans(high, Nat.add(c, high), k, Facts.le_add_cong(c, b, high, Api.le_add_left(c, b)), nested)
617      %Equal.sym(Array<F32>, spec(input, axes, fill, ops, k, inner, b), spec(input, axes, fill, ops, 1n+k, inner, b), below(input, axes, fill, ops, k, inner, b, low_h)) :
618        {ANode{_, spec(input, axes, fill, ops, k, inner, high)} == spec(input, axes, fill, ops, 1n+k, 1n+inner, b) : Array<F32>}
619      %Equal.sym(Array<F32>, spec(input, axes, fill, ops, k, inner, high), spec(input, axes, fill, ops, 1n+k, inner, high), below(input, axes, fill, ops, k, inner, high, nested)) :
620        {ANode{spec(input, axes, fill, ops, 1n+k, inner, b), _} == spec(input, axes, fill, ops, 1n+k, 1n+inner, b) : Array<F32>}
621      {==}