def entry_at

bendtorch-core@0.1.0.0 · src/tensor/gather_PROOF.bend:365

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

365def entry_at(+kind: Gather.Lookup, +outer: Nat, +rows: Nat, +inner: Nat, +count: Nat, +o: Nat, +k: Nat, +r: Nat,
366  +k_below: {Nat.is_lt(k, count) == True{} : Bool}, +r_below: {Nat.is_lt(r, inner) == True{} : Bool}) ->
367  {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}:
368  +row = Nat.add(Nat.mul(o, count), k)
369  +pos = Laws.position(count, inner, o, k, r)
370  %Equal.sym(Nat, Nat.div(pos, inner), row, BatchedProof.div_exact(row, inner, r, r_below)) :
371    {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}
372  %Equal.sym(Nat, Nat.mod(pos, inner), r, BatchedProof.mod_exact(row, inner, r, r_below)) :
373    {Gather.entry_of(kind, count, inner, Nat.div(row, count), Nat.mod(row, count), _) == Laws.entry_at(kind, count, inner, o, k, r) : Nat}
374  %Equal.sym(Nat, Nat.div(row, count), o, BatchedProof.div_exact(o, count, k, k_below)) :
375    {Gather.entry_of(kind, count, inner, _, Nat.mod(row, count), r) == Laws.entry_at(kind, count, inner, o, k, r) : Nat}
376  %Equal.sym(Nat, Nat.mod(row, count), k, BatchedProof.mod_exact(o, count, k, k_below)) :
377    {Gather.entry_of(kind, count, inner, o, _, r) == Laws.entry_at(kind, count, inner, o, k, r) : Nat}
378  entry_same(kind, count, inner, o, k, r)