def entry_read

bendtorch-core@0.1.0.0 · src/tensor/gather_PROOF.bend:393

import Base
import bendtorch-core@0.1.0.0/src/storage/model.bend as Model
import bendtorch-core@0.1.0.0/src/storage/refinement.bend as Refinement
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/parallel_proofs.bend as Generic

393# The entry the cell reads, as the laws name it, rewritten to the code's.
394def entry_read(+depth: Nat, +path: Model.Path(depth), +base: Nat, +kind: Gather.Lookup, +outer: Nat, +rows: Nat, +inner: Nat, +count: Nat,
395  +o: Nat, +k: Nat, +r: Nat, +k_below: {Nat.is_lt(k, count) == True{} : Bool}, +r_below: {Nat.is_lt(r, inner) == True{} : Bool},
396  +at: {Nat.add(Model.offset(depth, path), base) == Laws.position(count, inner, o, k, r) : Nat}, +di: Nat, -I: Array<U32>, +j: U32,
397  -read: {Model.observe(U32, di, I, Refinement.route(di, U32.from_nat(Laws.entry_at(kind, count, inner, o, k, r)))) == Some{j} : Maybe<&2, U32>}) ->
398  Generic.Fact<{Model.observe(U32, di, I, Refinement.route(di, U32.from_nat(Gather.entry(Gather.Plan{kind, outer, rows, inner, count}, Nat.add(Model.offset(depth, path), base))))) == Some{j} : Maybe<&2, U32>}>:
399  Generic.Fact{Equal.trans(Maybe<&2, U32>, Model.observe(U32, di, I, Refinement.route(di, U32.from_nat(Gather.entry(Gather.Plan{kind, outer, rows, inner, count}, Nat.add(Model.offset(depth, path), base))))),
400    Model.observe(U32, di, I, Refinement.route(di, U32.from_nat(Laws.entry_at(kind, count, inner, o, k, r)))), Some{j},
401    Equal.cong(Nat, Maybe<&2, U32>, e => Model.observe(U32, di, I, Refinement.route(di, U32.from_nat(e))), Gather.entry(Gather.Plan{kind, outer, rows, inner, count}, Nat.add(Model.offset(depth, path), base)), Laws.entry_at(kind, count, inner, o, k, r),
402      Equal.trans(Nat, Gather.entry(Gather.Plan{kind, outer, rows, inner, count}, Nat.add(Model.offset(depth, path), base)), 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),
403        Equal.cong(Nat, Nat, x => Gather.entry(Gather.Plan{kind, outer, rows, inner, count}, x), Nat.add(Model.offset(depth, path), base), Laws.position(count, inner, o, k, r), at),
404        entry_at(kind, outer, rows, inner, count, o, k, r, k_below, r_below))),
405    read)}