SlicePROOF.zero_head: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend as SlicePROOF
Lines 375-389 of bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice_PROOF.bend&start_line=375&end_line=389

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/storage/arith.bend as Arith
import bendtorch-core@0.1.0.0/src/tensor/slice.bend as Slice

# Some dimension 0 makes the element count 0.
def zero_head(+extent: U32, +rest: List<&2, U32>, h: {Slice.holds_zero(extent <> rest) == True{} : Bool},
  rec: @h: {Slice.holds_zero(rest) == True{} : Bool} -> {Shape.logical_numel(rest) == 0n : Nat},
  decision: Shape.BoolCase<Nat.is_eq(U32.to_nat(extent), 0n)>) -> {Shape.logical_numel(extent <> rest) == 0n : Nat}:
  match decision:
    case Shape.BTrue{equal}:
      %Equal.sym(Nat, U32.to_nat(extent), 0n, Arith.eq_true(U32.to_nat(extent), 0n, Equal.sym(Bool, True{}, Nat.is_eq(U32.to_nat(extent), 0n), equal))) :
        {Nat.mul(_, Shape.logical_numel(rest)) == 0n : Nat}
      {==}
    case Shape.BFalse{equal}:
      %Equal.sym(Nat, Shape.logical_numel(rest), 0n,
        rec(Equal.trans(Bool, Slice.holds_zero(rest), Bool.or(Nat.is_eq(U32.to_nat(extent), 0n), Slice.holds_zero(rest)), True{},
          Equal.cong(Bool, Bool, x => Bool.or(x, Slice.holds_zero(rest)), False{}, Nat.is_eq(U32.to_nat(extent), 0n), equal), h))) :
        {Nat.mul(U32.to_nat(extent), _) == 0n : Nat}
      Nats.mul_zero_right(U32.to_nat(extent))

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.or
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  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=BoolCase
  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/shape/nat_proofs.bend&name=mul_zero_right
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/arith.bend&name=eq_true
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/slice.bend&name=holds_zero