def left_below

bendtorch-core@0.1.0.0 · src/tensor/contracts/dot_proof.bend:65

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend as Nats
import bendtorch-core@0.1.0.0/src/tensor/contracts/dot.bend as Dot

65def left_below(+rows: Nat, +inner: Nat, +columns: Nat, +row: Nat, +column: Nat,
66  row_below: {Nat.is_lt(row, rows) == True{} : Bool}, +left: Shape.Shape,
67  left_extents: {Shape.extents(left) == [rows, inner] : List<&2, Nat>}, +k: Nat, below: {Nat.is_lt(k, inner) == True{} : Bool}) ->
68  {Nat.is_lt(Dot.left_index(Dot.Cell{row, column, inner, columns}, k), Shape.logical_numel(Shape.dimensions(left))) == True{} : Bool}:
69  %Equal.sym(List<&2, Nat>, Shape.extents(left), [rows, inner], left_extents) :
70    {Nat.is_lt(Nat.add(Nat.mul(row, inner), k), Shape.numel(_)) == True{} : Bool}
71  %Equal.sym(Nat, Nat.mul(inner, 1n), inner, Nats.mul_one_right(inner)) :
72    {Nat.is_lt(Nat.add(Nat.mul(row, inner), k), Nat.mul(rows, _)) == True{} : Bool}
73  lt_mul_add(row, rows, k, inner, row_below, below)