theorem
Hex.GraphIso.Nauty.Max.SweepInput.received_input
{n k : Nat}
{G : Colored n k}
{tcLevel fuel cfuel : Nat}
{first short : Bool}
{level numcells tc tv1 tv index : Nat}
{cell : VSet n}
{st out : Search n}
{l : Loop n}
{bs fs : List Nat}
{parents : Parents n}
(h :
SweepInput G { g := rowsOf G } tcLevel fuel (cfuel + 1) first level numcells tc tv1 (some tv) cell index st l bs fs
parents)
(hn : (contract G tcLevel).nodeValid fuel (Generic.nodeCall { g := rowsOf G } (n + 2) tcLevel fuel))
(hvisit : (!first || st.orbits[tv]! == tv) = true)
(hcall :
Nauty.node (first && tv == tv1) { g := rowsOf G } (n + 2) tcLevel fuel (level + 1) (numcells + 1)
(child first level tc tv st) = (Generic.Exit.unwind level short, out))
:
have ctx := { g := rowsOf G };
have middle := if (first && tv == tv1) = true then afterChildFirst level tv1 out else out;
have left :=
{ lab := middle.lab, ptn := middle.ptn, active := middle.active, orbits := middle.orbits,
fixedpts := middle.fixedpts.erase tv, autos := middle.autos, wsCap := middle.wsCap, firstcode := middle.firstcode,
canoncode := middle.canoncode, firsttc := middle.firsttc, firstlab := middle.firstlab, canonlab := middle.canonlab,
canong := middle.canong, samerows := middle.samerows, compCanon := middle.compCanon,
eqlevFirst := middle.eqlevFirst, eqlevCanon := middle.eqlevCanon, gcaFirst := middle.gcaFirst,
gcaCanon := middle.gcaCanon, canonlevel := middle.canonlevel, noncheaplevel := middle.noncheaplevel,
allsamelevel := middle.allsamelevel, cosetindex := middle.cosetindex, stabvertex := middle.stabvertex,
numnodes := middle.numnodes, tctotal := middle.tctotal, canupdates := middle.canupdates,
numorbits := middle.numorbits, numgenerators := middle.numgenerators, numbadleaves := middle.numbadleaves,
maxlevel := middle.maxlevel, order := middle.order, genTrace := middle.genTrace, workperm := middle.workperm };
have small := if short = true then shortprune cell left else cell;
have filtered := if (!first && tv == tv1) = true then longprune small left.fixedpts left.autos else small;
have ready := recover (n + 2) level left;
have nextIndex := if (first && ready.orbits[tv]! == tv1) = true then index + 1 else index;
(first = true →
∀ (γ : Array Nat),
γ ∈ ready.genTrace →
CellStab (Loop.prepare ctx tcLevel l).snd.snd.snd.snd.ptn level (Loop.prepare ctx tcLevel l).snd.snd.snd.snd.lab
γ) →
(∀ (t : Nat) (p : Parent n),
parents t = some p →
p.loop.first = true → ∀ (γ : Array Nat), γ ∈ ready.genTrace → CellStab p.state.ptn t p.state.lab γ) →
∃ (bs' : List Nat), ∃ (fs' : List Nat), SweepInput G ctx tcLevel fuel cfuel first level numcells tc tv1 (filtered.nextElem (some tv)) filtered nextIndex
ready l bs' fs' parents ∧ SearchState.best ctx ready = SearchState.key ctx bs' ready ∧ SearchState.best ctx out = SearchState.key ctx bs' ready
Reception constructs the complete suffix input from the actual child contract and return-local generator premises.