GatherPROOF.entry_at: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend as GatherPROOF
Lines 365-378 of bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend&start_line=365&end_line=378

import Base
import bendtorch-core@0.1.0.0/src/tensor/gather.bend as Gather
import bendtorch-core@0.1.0.0/src/tensor/gather_LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend as BatchedProof

def entry_at(+kind: Gather.Lookup, +outer: Nat, +rows: Nat, +inner: Nat, +count: Nat, +o: Nat, +k: Nat, +r: Nat,
  +k_below: {Nat.is_lt(k, count) == True{} : Bool}, +r_below: {Nat.is_lt(r, inner) == True{} : Bool}) ->
  {Gather.entry(Gather.Plan{kind, outer, rows, inner, count}, Laws.position(count, inner, o, k, r)) == Laws.entry_at(kind, count, inner, o, k, r) : Nat}:
  +row = Nat.add(Nat.mul(o, count), k)
  +pos = Laws.position(count, inner, o, k, r)
  %Equal.sym(Nat, Nat.div(pos, inner), row, BatchedProof.div_exact(row, inner, r, r_below)) :
    {Gather.entry_of(kind, count, inner, Nat.div(_, count), Nat.mod(_, count), Nat.mod(pos, inner)) == Laws.entry_at(kind, count, inner, o, k, r) : Nat}
  %Equal.sym(Nat, Nat.mod(pos, inner), r, BatchedProof.mod_exact(row, inner, r, r_below)) :
    {Gather.entry_of(kind, count, inner, Nat.div(row, count), Nat.mod(row, count), _) == Laws.entry_at(kind, count, inner, o, k, r) : Nat}
  %Equal.sym(Nat, Nat.div(row, count), o, BatchedProof.div_exact(o, count, k, k_below)) :
    {Gather.entry_of(kind, count, inner, _, Nat.mod(row, count), r) == Laws.entry_at(kind, count, inner, o, k, r) : Nat}
  %Equal.sym(Nat, Nat.mod(row, count), k, BatchedProof.mod_exact(o, count, k, k_below)) :
    {Gather.entry_of(kind, count, inner, o, _, r) == Laws.entry_at(kind, count, inner, o, k, r) : Nat}
  entry_same(kind, count, inner, o, k, r)

Uses (17):
  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=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=Nat.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend&name=div_exact
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/batched_matmul_PROOF.bend&name=mod_exact
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=Lookup
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=Plan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=entry
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=entry_of
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_LAWS.bend&name=entry_at
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_LAWS.bend&name=position
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend&name=entry_same