import JaxLean.Stdlib import examples.tensor_puzzles.generated.PuzzlesCumsumset_option maxRecDepth 4096set_option maxHeartbeats 2000000namespace JaxLean.Puzzles.Cumsumtheorem matches_loop (a : Tensor ℝ [3]) : Array.cumsum a = Loop.cumsum a := bya:Tensor ℝ [3]⊢ Array.cumsum a = Loop.cumsum a funext ⟨i, u⟩a:Tensor ℝ [3]i:Fin 3u:Index []⊢ Array.cumsum a (i, u) = Loop.cumsum a (i, u) cases uunita:Tensor ℝ [3]i:Fin 3⊢ Array.cumsum a (i, PUnit.unit) = Loop.cumsum a (i, PUnit.unit) fin_cases iunit.«0»a:Tensor ℝ [3]⊢ Array.cumsum a ((fun i => i) ⟨0, ⋯⟩, PUnit.unit) = Loop.cumsum a ((fun i => i) ⟨0, ⋯⟩, PUnit.unit)unit.«1»a:Tensor ℝ [3]⊢ Array.cumsum a ((fun i => i) ⟨1, ⋯⟩, PUnit.unit) = Loop.cumsum a ((fun i => i) ⟨1, ⋯⟩, PUnit.unit)unit.«2»a:Tensor ℝ [3]⊢ Array.cumsum a ((fun i => i) ⟨2, ⋯⟩, PUnit.unit) = Loop.cumsum a ((fun i => i) ⟨2, ⋯⟩, PUnit.unit) <;>unit.«0»a:Tensor ℝ [3]⊢ Array.cumsum a ((fun i => i) ⟨0, ⋯⟩, PUnit.unit) = Loop.cumsum a ((fun i => i) ⟨0, ⋯⟩, PUnit.unit)unit.«1»a:Tensor ℝ [3]⊢ Array.cumsum a ((fun i => i) ⟨1, ⋯⟩, PUnit.unit) = Loop.cumsum a ((fun i => i) ⟨1, ⋯⟩, PUnit.unit)unit.«2»a:Tensor ℝ [3]⊢ Array.cumsum a ((fun i => i) ⟨2, ⋯⟩, PUnit.unit) = Loop.cumsum a ((fun i => i) ⟨2, ⋯⟩, PUnit.unit) simp only [Array.fn__where, Array.puzzle_cumsum, Array.cumsum, Loop.cumsum, Tensor.scalar, Tensor.reindex, Tensor.scatterSet_vector, Fin.sum_univ_succ]unit.«2»a:Tensor ℝ [3]⊢ (if decide (↑2 ≥ ↑↑0) = true then a (0, ()) else 0) + ((if decide (↑2 ≥ ↑↑(Fin.succ 0)) = true then a (Fin.succ 0, ()) else 0) + ((if decide (↑2 ≥ ↑↑(Fin.succ 0).succ) = true then a ((Fin.succ 0).succ, ()) else 0) + ∑ x, if decide (↑2 ≥ ↑↑x.succ.succ.succ) = true then a (x.succ.succ.succ, ()) else 0)) = if ⟨2, ⋯⟩ = 2 then 0 + a (⟨0 + 1 * ↑0, ⋯⟩, ()) + a (⟨1 + 1 * ↑0, ⋯⟩, ()) + a (⟨2 + 1 * ↑0, ⋯⟩, ()) else if ⟨2, ⋯⟩ = 1 then 0 + a (⟨0 + 1 * ↑0, ⋯⟩, ()) + a (⟨1 + 1 * ↑0, ⋯⟩, ()) else if ⟨2, ⋯⟩ = 0 then 0 + a (⟨0 + 1 * ↑0, ⋯⟩, ()) else 0 all_goals norm_num [Fin.ext_iff, Bool.cond_decide, decide_eq_true_iff]unit.«2»a:Tensor ℝ [3]⊢ a (0, ()) + (a (1, ()) + a (2, ())) = a (0, ()) + a (1, ()) + a (⟨2, ⋯⟩, ()) all_goals simp []unit.«2»a:Tensor ℝ [3]⊢ a (0, ()) + (a (1, ()) + a (2, ())) = a (0, ()) + a (1, ()) + a (2, ()) all_goals ringAll goals completed! 🐙 theorem certificate (a : Tensor ℝ [3]) : Jaxpr.Program.eval (.cons a .nil) Array.cumsum_ir = Jaxpr.Program.eval (.cons a .nil) Loop.cumsum_ir := bya:Tensor ℝ [3]⊢ Jaxpr.Program.eval (Jaxpr.Env.cons a Jaxpr.Env.nil) Array.cumsum_ir = Jaxpr.Program.eval (Jaxpr.Env.cons a Jaxpr.Env.nil) Loop.cumsum_ir rw [Array.cumsum_translation_correct,a:Tensor ℝ [3]⊢ Array.cumsum a = Jaxpr.Program.eval (Jaxpr.Env.cons a Jaxpr.Env.nil) Loop.cumsum_ira:Tensor ℝ [3]⊢ Array.cumsum a = Loop.cumsum a Loop.cumsum_translation_correcta:Tensor ℝ [3]⊢ Array.cumsum a = Loop.cumsum aa:Tensor ℝ [3]⊢ Array.cumsum a = Loop.cumsum a]a:Tensor ℝ [3]⊢ Array.cumsum a = Loop.cumsum a exact matches_loop aAll goals completed! 🐙end JaxLean.Puzzles.Cumsum