PermuteBuildProof.pair_join_eq: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/permute_build_proof.bend as PermuteBuildProof
Lines 745-753 of bendtorch-core@0.1.0.0/src/tensor/permute_build_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/permute_build_proof.bend&start_line=745&end_line=753

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/layout.bend as Layout
import bendtorch-core@0.1.0.0/src/storage/main.bend as Storage
import bendtorch-core@0.1.0.0/src/tensor/parallel.bend as Parallel
import bendtorch-core@0.1.0.0/src/storage/LAWS.bend as StorageLaws

def pair_join_eq(+input: Shape.Shape, +axes: List<&2, U32>, +fill: F32, +ops: List<&2, StorageLaws.Op>, +plan: Layout.Plan<input, axes>, +ds: Nat, +fits: {Storage.bounds(ds, U32.to_nat(Shape.count(input))) == True{} : Bool}, +count: Nat, +exact: {count == Shape.logical_numel(Shape.dimensions(Layout.output(input, axes, plan))) : Nat}, +base: Nat, x: F32, high: F32 & (Array<F32> & Array<F32>),
  ex: {ALeaf{x} == spec(input, axes, fill, ops, count, 0n, base) : Array<F32>},
  leaf_facts: TreeEq(input, axes, fill, ops, plan, ds, fits, count, exact, 0n, Nat.add(1n, base), Parallel.leaf(~(Array<F32> & Array<F32>), high))) ->
  TreeEq(input, axes, fill, ops, plan, ds, fits, count, exact, 1n, base, Parallel.pair_join(~(Array<F32> & Array<F32>), x, high)):
  (y, inputs) = high
  (ey, kept) = leaf_facts
  (%Equal.sym(Array<F32>, ALeaf{x}, spec(input, axes, fill, ops, count, 0n, base), ex) : {ANode{_, ALeaf{y}} == ANode{spec(input, axes, fill, ops, count, 0n, base), spec(input, axes, fill, ops, count, 0n, Nat.add(1n, base))} : Array<F32>}
   %Equal.sym(Array<F32>, ALeaf{y}, spec(input, axes, fill, ops, count, 0n, Nat.add(1n, base)), ey) : {ANode{spec(input, axes, fill, ops, count, 0n, base), _} == ANode{spec(input, axes, fill, ops, count, 0n, base), spec(input, axes, fill, ops, count, 0n, Nat.add(1n, base))} : Array<F32>}
   {==}, kept)

Uses (23):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=count
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=dimensions
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=logical_numel
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/LAWS.bend&name=Op
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/main.bend&name=bounds
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/layout.bend&name=Plan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/layout.bend&name=output
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/parallel.bend&name=leaf
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/parallel.bend&name=pair_join
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/permute_build_proof.bend&name=TreeEq
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/permute_build_proof.bend&name=spec