task_id stringlengths 21 23 | challenge_id stringlengths 16 16 | proof_assistant stringclasses 1
value | session stringclasses 1
value | repo stringclasses 57
values | revision stringclasses 57
values | file_path stringlengths 13 92 | theory stringlengths 1 48 | variant int64 0 132 | challenge_type stringclasses 1
value | difficulty null | count null | by_centrality bool 1
class | ablation_prob float64 0.5 0.5 | min_depth int64 1 1 | max_depth int64 1 1 | leaves_only bool 1
class | min_size int64 0 0 | max_size stringclasses 1
value | min_centrality int64 0 0 | max_centrality stringclasses 1
value | seed int64 42 42 | n_proofs int64 1 173 | n_ablated int64 1 60 | holes_filled listlengths 1 60 | deleted_lemmas listlengths 1 1 | corollaries listlengths 1 1 | closure_size int64 1 172 | challenge_file_content stringlengths 133 350k | solution_file_content stringlengths 394 351k | solution_diff stringlengths 243 134k | manifest dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ablate_0c2aef1520be_2 | c716f9d0c1e9ac68 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/GaussPeriodicity.lean | GaussPeriodicity | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "gauss_sum_1_periodic",
"depth": 1,
"n_commands": 0,
"n_lines": 71,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have A : ∀ n : ℤ, (gauss_term_ℝ σ (μ + 1)) n = (gauss_term_ℝ σ μ) (n - 1) := by\n intro n ; simp [gauss_term_ℝ, ga... | [
{
"name": "shifted_gauss_summable_neg",
"text": "/--\n``gauss_term_ℝ`` is summable under any shift.\n-/\ntheorem shifted_gauss_summable_neg {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) (k : ℤ) :\n Summable fun (n : ℕ) => (gauss_term_ℝ σ μ) ((-(n + k)) : ℤ) := by\n conv =>\n arg 1\n intro n\n rw [shifted_gauss_mea... | [
{
"name": "gauss_sum_1_periodic",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 77,
"n_chars": 2422,
"n_subproofs": 17,
"n_tactics": 65,
"cyclomatic": 1,
"n_automation": 12,
"n_rewrites": 12,
"n_structural": 13,
"automation_only": false,
... | 4 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.GaussConvergence
/-!
# Discrete Gaussian Periodicity
This file contains lemmas related to the periodicity o... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.GaussConvergence
/-!
# Discrete Gaussian Periodicity
This file contains lemmas related to the periodicity o... | @@ -40,9 +40,90 @@
apply gauss_convergence_nat_pos h
/--
+``gauss_term_ℝ`` is summable under any shift.
+-/
+theorem shifted_gauss_summable_neg {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) (k : ℤ) :
+ Summable fun (n : ℕ) => (gauss_term_ℝ σ μ) ((-(n + k)) : ℤ) := by
+ conv =>
+ arg 1
+ intro n
+ rw [shifted_gauss_mean_... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_0c2aef1520be_3 | af95e8f884363157 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/GaussPeriodicity.lean | GaussPeriodicity | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "shifted_gauss_sum_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n revert μ\n induction k\n · simp\n · intro μ\n rename_i n IH\n simp\n rw [← add_assoc]\n rw [IH]\n ... | [
{
"name": "gauss_sum_1_periodic",
"text": "/--\nThe sum of ``gauss_term_ℝ`` does not change when the mean shifts by 1.\n-/\ntheorem gauss_sum_1_periodic {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) :\n (∑' (n : ℤ), (gauss_term_ℝ σ μ) n) = ∑' (n : ℤ), (gauss_term_ℝ σ (μ + 1)) n := by\n have A : ∀ n : ℤ, (gauss_term_ℝ σ (μ ... | [
{
"name": "shifted_gauss_sum_pos",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 16,
"n_chars": 421,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": false,
"max... | 5 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.GaussConvergence
/-!
# Discrete Gaussian Periodicity
This file contains lemmas related to the periodicity o... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.GaussConvergence
/-!
# Discrete Gaussian Periodicity
This file contains lemmas related to the periodicity o... | @@ -51,6 +51,82 @@
apply gauss_convergence_nat_pos h
/--
+The sum of ``gauss_term_ℝ`` does not change when the mean shifts by 1.
+-/
+theorem gauss_sum_1_periodic {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) :
+ (∑' (n : ℤ), (gauss_term_ℝ σ μ) n) = ∑' (n : ℤ), (gauss_term_ℝ σ (μ + 1)) n := by
+ have A : ∀ n : ℤ, (gauss_term_ℝ σ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_0c2aef1520be_4 | b06898cea8eeb17a | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/GaussPeriodicity.lean | GaussPeriodicity | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "shifted_gauss_sum_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n revert μ\n induction k\n · simp\n · intro μ\n rename_i n IH\n simp\n rw [← add_assoc]\n rw [IH]\n ... | [
{
"name": "gauss_sum_1_periodic",
"text": "/--\nThe sum of ``gauss_term_ℝ`` does not change when the mean shifts by 1.\n-/\ntheorem gauss_sum_1_periodic {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) :\n (∑' (n : ℤ), (gauss_term_ℝ σ μ) n) = ∑' (n : ℤ), (gauss_term_ℝ σ (μ + 1)) n := by\n have A : ∀ n : ℤ, (gauss_term_ℝ σ (μ ... | [
{
"name": "shifted_gauss_sum_neg",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 20,
"n_chars": 506,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": false,
"max... | 5 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.GaussConvergence
/-!
# Discrete Gaussian Periodicity
This file contains lemmas related to the periodicity o... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.GaussConvergence
/-!
# Discrete Gaussian Periodicity
This file contains lemmas related to the periodicity o... | @@ -51,6 +51,82 @@
apply gauss_convergence_nat_pos h
/--
+The sum of ``gauss_term_ℝ`` does not change when the mean shifts by 1.
+-/
+theorem gauss_sum_1_periodic {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) :
+ (∑' (n : ℤ), (gauss_term_ℝ σ μ) n) = ∑' (n : ℤ), (gauss_term_ℝ σ (μ + 1)) n := by
+ have A : ∀ n : ℤ, (gauss_term_ℝ σ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_0c2aef1520be_5 | da4e8c376fb07bb8 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/GaussPeriodicity.lean | GaussPeriodicity | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "shifted_gauss_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases k\n · apply shifted_gauss_sum_pos h\n · simp\n have X : ∀ a : ℕ, -(1: ℝ) + -a = - (((1 + a) : ℕ)) := by\n ... | [
{
"name": "shifted_gauss_sum_neg",
"text": "/--\nThe sum of ``gauss_term_ℝ`` does not change when the mean shifts by a negative integer.\n-/\ntheorem shifted_gauss_sum_neg {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) (k : ℕ) :\n (∑' (n : ℤ), (gauss_term_ℝ σ μ) n) = ∑' (n : ℤ), (gauss_term_ℝ σ (μ - k)) n := by\n revert μ\n... | [
{
"name": "shifted_gauss_sum",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 7,
"n_lines": 17,
"n_chars": 514,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false,
"max_nes... | 7 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.GaussConvergence
/-!
# Discrete Gaussian Periodicity
This file contains lemmas related to the periodicity o... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.GaussConvergence
/-!
# Discrete Gaussian Periodicity
This file contains lemmas related to the periodicity o... | @@ -142,12 +142,38 @@
rw [gauss_sum_1_periodic h]
/--
+The sum of ``gauss_term_ℝ`` does not change when the mean shifts by a negative integer.
+-/
+theorem shifted_gauss_sum_neg {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) (k : ℕ) :
+ (∑' (n : ℤ), (gauss_term_ℝ σ μ) n) = ∑' (n : ℤ), (gauss_term_ℝ σ (μ - k)) n := by
+ revert μ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_0c2aef1520be_6 | 2d5c76144fbe6c8e | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/GaussPeriodicity.lean | GaussPeriodicity | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "shifted_gauss_sum_0",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have X := shifted_gauss_sum h 0 μ\n rw [X]\n simp",
"n_chars": 56,
"n_subproofs": 1,
"n_tactics": 4,
... | [
{
"name": "shifted_gauss_sum",
"text": "/--\nThe sum of ``gauss_term_ℝ`` does not change when the mean shifts by any integer.\n-/\ntheorem shifted_gauss_sum {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) (k : ℤ) :\n (∑' (n : ℤ), (gauss_term_ℝ σ μ) n) = ∑' (n : ℤ), (gauss_term_ℝ σ (μ + k)) n := by\n cases k\n · apply shifte... | [
{
"name": "shifted_gauss_sum_0",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 8,
"n_lines": 9,
"n_chars": 297,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nes... | 8 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.GaussConvergence
/-!
# Discrete Gaussian Periodicity
This file contains lemmas related to the periodicity o... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.GaussConvergence
/-!
# Discrete Gaussian Periodicity
This file contains lemmas related to the periodicity o... | @@ -161,8 +161,27 @@
simp
/--
+The sum of ``gauss_term_ℝ`` does not change when the mean shifts by any integer.
+-/
+theorem shifted_gauss_sum {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) (k : ℤ) :
+ (∑' (n : ℤ), (gauss_term_ℝ σ μ) n) = ∑' (n : ℤ), (gauss_term_ℝ σ (μ + k)) n := by
+ cases k
+ · apply shifted_gauss_sum_pos h
... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_eb8d55b97f0d_1 | 3cd38e359fad445f | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Gaussian/Properties.lean | Properties | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "DiscreteGaussianSample_apply",
"depth": 1,
"n_commands": 0,
"n_lines": 116,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold discrete_gaussian\n unfold gauss_term_ℝ\n simp\n simp only [DiscreteGaussianSample, Bind.bind, Pur... | [
{
"name": "DiscreteGaussianSampleLoop_apply_true",
"text": "/--\nEvaluation of the discrete Gaussian sample loop distribution when the termination flag is ``true``.\n-/\n@[simp]\ntheorem DiscreteGaussianSampleLoop_apply_true (num den t : ℕ+) (n : ℤ) (mix : ℕ) :\n (DiscreteGaussianSampleLoop num den t mix) ... | [
{
"name": "DiscreteGaussianSample_apply",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 9,
"n_lines": 124,
"n_chars": 3992,
"n_subproofs": 7,
"n_tactics": 113,
"cyclomatic": 3,
"n_automation": 24,
"n_rewrites": 38,
"n_structural": 21,
"automation_only": fa... | 8 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic
import SampCert.Samplers.... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic
import SampCert.Samplers.... | @@ -105,6 +105,39 @@
subst h
contradiction
+/--
+Evaluation of the discrete Gaussian sample loop distribution when the termination flag is ``true``.
+-/
+@[simp]
+theorem DiscreteGaussianSampleLoop_apply_true (num den t : ℕ+) (n : ℤ) (mix : ℕ) :
+ (DiscreteGaussianSampleLoop num den t mix) (n, true)
+ =... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b8089d2cf53f_0 | b1a57470da136dfc | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Generic.lean | Generic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "privComposeChainRule",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros u v\n rw [<- compose_sum_rw_adaptive]\n simp [privComposeAdaptive]\n simp [DFunLike.coe]",
"n_chars": 10... | [
{
"name": "compose_sum_rw_adaptive",
"text": "lemma compose_sum_rw_adaptive (nq1 : List T → SPMF U) (nq2 : U -> List T → SPMF V) (u : U) (v : V) (l : List T) :\n (∑' (a : U), nq1 l a * ∑' (a_1 : V), if u = a ∧ v = a_1 then nq2 a l a_1 else 0) = nq1 l u * nq2 u l v := by\n have hrw1 : ∀ (a : U), nq1 l a * ... | [
{
"name": "privComposeChainRule",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 737,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import SampCert.DifferentialPrivacy.Sensitivity
import SampCert.Foundations.Basic
/-!
# Differential Privacy
This f... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import SampCert.DifferentialPrivacy.Sensitivity
import SampCert.Foundations.Basic
/-!
# Differential Privacy
This f... | @@ -87,13 +87,45 @@
coe p a := p.1 a
coe_injective' _ _ h := Subtype.ext h
+lemma compose_sum_rw_adaptive (nq1 : List T → SPMF U) (nq2 : U -> List T → SPMF V) (u : U) (v : V) (l : List T) :
+ (∑' (a : U), nq1 l a * ∑' (a_1 : V), if u = a ∧ v = a_1 then nq2 a l a_1 else 0) = nq1 l u * nq2 u l v := by
+ have hr... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b8089d2cf53f_1 | 58ba64407a9fb7f1 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Generic.lean | Generic | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "ENNReal.tsum_fiberwise",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply HasSum.tsum_eq\n apply ENNReal.HasSum_fiberwise\n apply Summable.hasSum\n exact ENNReal.summable",
"n_c... | [
{
"name": "ENNReal.HasSum_fiberwise",
"text": "/--\nPartition series into fibers. `g` maps an element to its fiber.\n-/\ntheorem ENNReal.HasSum_fiberwise {f : T → ENNReal} {a : ENNReal} (hf : HasSum f a) (g : T → V) :\n HasSum (fun c : V ↦ ∑' b : g ⁻¹' {c}, f b) a := by\n let A := (Equiv.sigmaFiberEquiv... | [
{
"name": "ENNReal.tsum_fiberwise",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 319,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import SampCert.DifferentialPrivacy.Sensitivity
import SampCert.Foundations.Basic
/-!
# Differential Privacy
This f... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import SampCert.DifferentialPrivacy.Sensitivity
import SampCert.Foundations.Basic
/-!
# Differential Privacy
This f... | @@ -90,9 +90,27 @@
/--
Partition series into fibers. `g` maps an element to its fiber.
-/
+theorem ENNReal.HasSum_fiberwise {f : T → ENNReal} {a : ENNReal} (hf : HasSum f a) (g : T → V) :
+ HasSum (fun c : V ↦ ∑' b : g ⁻¹' {c}, f b) a := by
+ let A := (Equiv.sigmaFiberEquiv g)
+ have B := @Equiv.hasSum_iff ENNR... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b8089d2cf53f_2 | 2f80c9a68141839e | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Generic.lean | Generic | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "ENNReal.tsum_fiberwise",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply HasSum.tsum_eq\n apply ENNReal.HasSum_fiberwise\n apply Summable.hasSum\n exact ENNReal.summable",
"n_c... | [
{
"name": "ENNReal.HasSum_fiberwise",
"text": "/--\nPartition series into fibers. `g` maps an element to its fiber.\n-/\ntheorem ENNReal.HasSum_fiberwise {f : T → ENNReal} {a : ENNReal} (hf : HasSum f a) (g : T → V) :\n HasSum (fun c : V ↦ ∑' b : g ⁻¹' {c}, f b) a := by\n let A := (Equiv.sigmaFiberEquiv... | [
{
"name": "fiberwisation",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 29,
"n_chars": 611,
"n_subproofs": 1,
"n_tactics": 22,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 5,
"n_structural": 6,
"automation_only": false,
"max_nesting... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import SampCert.DifferentialPrivacy.Sensitivity
import SampCert.Foundations.Basic
/-!
# Differential Privacy
This f... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import SampCert.DifferentialPrivacy.Sensitivity
import SampCert.Foundations.Basic
/-!
# Differential Privacy
This f... | @@ -90,9 +90,27 @@
/--
Partition series into fibers. `g` maps an element to its fiber.
-/
+theorem ENNReal.HasSum_fiberwise {f : T → ENNReal} {a : ENNReal} (hf : HasSum f a) (g : T → V) :
+ HasSum (fun c : V ↦ ∑' b : g ⁻¹' {c}, f b) a := by
+ let A := (Equiv.sigmaFiberEquiv g)
+ have B := @Equiv.hasSum_iff ENNR... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_44767fbddf81_0 | 4f273a96261be927 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Util.lean | Util | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "tsum_split_ite",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have B := @Summable.tsum_add_tsum_compl ENNReal T _ _ (fun i => if cond i then f i else g i) _ _ { i : T | cond i} ENNReal.s... | [
{
"name": "tsum_simpl_ite_right",
"text": "/--\nSimplify guarded series when series indices never satisfy the guard\n-/\ntheorem tsum_simpl_ite_right (cond : T → Bool) (f g : T → ENNReal) :\n (∑' (x : { i : T | ¬ cond i}), if cond x then f x else g x)\n = ((∑' (x : { i : T | ¬ cond i}), g x)) := by\n a... | [
{
"name": "tsum_split_ite",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 15,
"n_chars": 575,
"n_subproofs": 2,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 1,
"automation_only": false,
"max_nesting... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import Mathlib.Topology.Algebra.InfiniteSum.Basic
/-!
# Util
This file contains general SampCert utility lemmas
-/
... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import Mathlib.Topology.Algebra.InfiniteSum.Basic
/-!
# Util
This file contains general SampCert utility lemmas
-/
... | @@ -53,10 +53,34 @@
simp [A] at h
/--
+Simplify guarded series when series indices never satisfy the guard
+-/
+theorem tsum_simpl_ite_right (cond : T → Bool) (f g : T → ENNReal) :
+ (∑' (x : { i : T | ¬ cond i}), if cond x then f x else g x)
+ = ((∑' (x : { i : T | ¬ cond i}), g x)) := by
+ apply tsum_con... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_44767fbddf81_1 | 6cfe8826f506fedc | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Util.lean | Util | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "tsum_split_ite'",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have B := @Summable.tsum_add_tsum_compl ENNReal T _ _ (fun i => if cond i = false then f i else g i) _ _ { i : T | cond i ... | [
{
"name": "tsum_simpl_ite_right'",
"text": "/--\nSimplify guarded series based on index type\n-/\ntheorem tsum_simpl_ite_right' (cond : T → Bool) (f g : T → ENNReal) :\n (∑' (x : { i : T | cond i = false}), if cond x = false then f x else g x)\n = ((∑' (x : { i : T | cond i = false}), f x)) := by\n app... | [
{
"name": "tsum_split_ite'",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 649,
"n_subproofs": 2,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 1,
"automation_only": false,
"max_nesti... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import Mathlib.Topology.Algebra.InfiniteSum.Basic
/-!
# Util
This file contains general SampCert utility lemmas
-/
... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import Mathlib.Topology.Algebra.InfiniteSum.Basic
/-!
# Util
This file contains general SampCert utility lemmas
-/
... | @@ -53,10 +53,36 @@
· simp
/--
+Simplify guarded series based on index type
+-/
+theorem tsum_simpl_ite_right' (cond : T → Bool) (f g : T → ENNReal) :
+ (∑' (x : { i : T | cond i = false}), if cond x = false then f x else g x)
+ = ((∑' (x : { i : T | cond i = false}), f x)) := by
+ apply tsum_congr
+ intro ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_44767fbddf81_2 | 31382200e97b1e0e | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Util.lean | Util | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "tsum_split_coe_right",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [tsum_split_ite]\n simp",
"n_chars": 32,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n... | [
{
"name": "tsum_split_ite",
"text": "/--\nPartition series indices based on conditional guard\n-/\ntheorem tsum_split_ite (cond : T → Bool) (f g : T → ENNReal) :\n (∑' (i : T), if cond i then f i else g i)\n = (∑' (i : { i : T | cond i}), f i) + (∑' (i : { i : T | ¬ cond i}), g i) := by\n have B := @Su... | [
{
"name": "tsum_split_coe_right",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 10,
"n_chars": 262,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_n... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import Mathlib.Topology.Algebra.InfiniteSum.Basic
/-!
# Util
This file contains general SampCert utility lemmas
-/
... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import Mathlib.Topology.Algebra.InfiniteSum.Basic
/-!
# Util
This file contains general SampCert utility lemmas
-/
... | @@ -70,10 +70,26 @@
· simp
/--
+Partition series indices based on conditional guard
+-/
+theorem tsum_split_ite (cond : T → Bool) (f g : T → ENNReal) :
+ (∑' (i : T), if cond i then f i else g i)
+ = (∑' (i : { i : T | cond i}), f i) + (∑' (i : { i : T | ¬ cond i}), g i) := by
+ have B := @Summable.tsum_add_... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_44767fbddf81_3 | 91d984f7d9adf5f4 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Util.lean | Util | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "tsum_split_coe_left",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [tsum_split_ite']\n simp",
"n_chars": 33,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n... | [
{
"name": "tsum_split_ite'",
"text": "/--\nPartition series indices based on negation of conditional guard\n-/\ntheorem tsum_split_ite' (cond : T → Bool) (f g : T → ENNReal) :\n (∑' (i : T), if cond i = false then f i else g i)\n = (∑' (i : { i : T | cond i = false}), f i) + (∑' (i : { i : T | cond i = ... | [
{
"name": "tsum_split_coe_left",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 10,
"n_chars": 264,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_ne... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import Mathlib.Topology.Algebra.InfiniteSum.Basic
/-!
# Util
This file contains general SampCert utility lemmas
-/
... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import Mathlib.Topology.Algebra.InfiniteSum.Basic
/-!
# Util
This file contains general SampCert utility lemmas
-/
... | @@ -70,10 +70,28 @@
simp [A] at h
/--
+Partition series indices based on negation of conditional guard
+-/
+theorem tsum_split_ite' (cond : T → Bool) (f g : T → ENNReal) :
+ (∑' (i : T), if cond i = false then f i else g i)
+ = (∑' (i : { i : T | cond i = false}), f i) + (∑' (i : { i : T | cond i = true}), ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_44767fbddf81_4 | aa7b87d7df6127b1 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Util.lean | Util | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "tsum_split_less",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have A := @Summable.tsum_add_tsum_compl ENNReal ℕ _ _ f _ _ { i : ℕ | cond i} ENNReal.summable ENNReal.summable\n rw [← A]... | [
{
"name": "tsum_split_coe_right",
"text": "/--\nAdd vacuous guard to series based on index type\n-/\ntheorem tsum_split_coe_right (cond : T → Bool) (f : T → ENNReal) :\n (∑' (i : { i : T | cond i = true}), f i)\n = (∑' (i : T), if cond i = true then f i else 0) := by\n rw [tsum_split_ite]\n simp\n\n",... | [
{
"name": "tsum_split_less",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 11,
"n_chars": 379,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 4 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import Mathlib.Topology.Algebra.InfiniteSum.Basic
/-!
# Util
This file contains general SampCert utility lemmas
-/
... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.SLang
import Mathlib.Topology.Algebra.InfiniteSum.Basic
/-!
# Util
This file contains general SampCert utility lemmas
-/
... | @@ -84,9 +84,22 @@
rw [tsum_simpl_ite_right]
/--
+Add vacuous guard to series based on index type
+-/
+theorem tsum_split_coe_right (cond : T → Bool) (f : T → ENNReal) :
+ (∑' (i : { i : T | cond i = true}), f i)
+ = (∑' (i : T), if cond i = true then f i else 0) := by
+ rw [tsum_split_ite]
+ simp
+
+/--
B... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_98f363603580_0 | c9c11271e5154fb9 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Foundations/Until.lean | Until | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "probUntilCut_apply_unsat",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n revert i\n induction fuel\n · simp only [probUntilCut_zero, implies_true]\n · rename_i fuel IH\n intro j\n ... | [
{
"name": "probUntilCut_zero",
"text": "/--\nTruncation of ``probUntil`` program to zero unrollings is identically zero.\n-/\n@[simp]\ntheorem probUntilCut_zero (st : T) (body : SLang T) (cond : T → Bool) (x : T) :\n probWhileCut (fun v => decide (cond v = false)) (fun _ => body) 0 st x = 0 := by\n simp [... | [
{
"name": "probUntilCut_apply_unsat",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 25,
"n_chars": 764,
"n_subproofs": 0,
"n_tactics": 17,
"cyclomatic": 4,
"n_automation": 6,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.While
import SampCert.Util.Util
/-!
# ``probUntil`` Properties
This file proves evaluation and normalization ... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.While
import SampCert.Util.Util
/-!
# ``probUntil`` Properties
This file proves evaluation and normalization ... | @@ -27,6 +27,14 @@
variable {T : Type}
/--
+Truncation of ``probUntil`` program to zero unrollings is identically zero.
+-/
+@[simp]
+theorem probUntilCut_zero (st : T) (body : SLang T) (cond : T → Bool) (x : T) :
+ probWhileCut (fun v => decide (cond v = false)) (fun _ => body) 0 st x = 0 := by
+ simp [probWhile... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_a25cb1f21718_0 | f14fc9828ba41c8c | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/Const.lean | Const | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "privConst_zCDP",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [zCDP] at *\n intro u\n apply And.intro\n · apply privConst_AC\n · apply privConst_zCDPBound",
"n_chars": 105,
... | [
{
"name": "privConst_zCDPBound",
"text": "/--\nConstant query satisfies zCDP Renyi divergence bound.\n-/\ntheorem privConst_zCDPBound {u : U} : zCDPBound (privConst u : Mechanism T U) 0 := by\n simp [zCDPBound, privConst]\n intros\n refine (RenyiDivergence_aux_zero (PMF.pure u) (PMF.pure u) ?G1 fun x a =... | [
{
"name": "privConst_zCDP",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 240,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# zCDP Constant function
This fil... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# zCDP Constant function
This fil... | @@ -25,6 +25,15 @@
variable [Countable U]
/--
+Constant query satisfies zCDP Renyi divergence bound.
+-/
+theorem privConst_zCDPBound {u : U} : zCDPBound (privConst u : Mechanism T U) 0 := by
+ simp [zCDPBound, privConst]
+ intros
+ refine (RenyiDivergence_aux_zero (PMF.pure u) (PMF.pure u) ?G1 fun x a => a).mp ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_c8b50995280b_0 | 5d1d1f80b50ecf0a | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Pure/Par.lean | Par | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "pureDP_priv_Par",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n (· ▸ privParCompose_DP_Bound)",
"n_chars": 35,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_autom... | [
{
"name": "privParCompose_DP_Bound",
"text": "theorem privParCompose_DP_Bound {m1 : Mechanism T U} {m2 : Mechanism T V} {ε₁ ε₂ : NNReal} (f)\n (H1 : DP m1 ε₁) (H2 : DP m2 ε₂) : DP (privParCompose m1 m2 f) (max ε₁ ε₂) := by\n\n apply singleton_to_event\n apply event_to_singleton at H1\n apply event_to_... | [
{
"name": "pureDP_priv_Par",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 227,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.Pure.DP
/-!
# Pure DP parallel composition
This file proves ... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.Pure.DP
/-!
# Pure DP parallel composition
This file proves ... | @@ -19,8 +19,122 @@
namespace SLang
-- FIXME: Cleanup!
+theorem privParCompose_DP_Bound {m1 : Mechanism T U} {m2 : Mechanism T V} {ε₁ ε₂ : NNReal} (f)
+ (H1 : DP m1 ε₁) (H2 : DP m2 ε₂) : DP (privParCompose m1 m2 f) (max ε₁ ε₂) := by
+
+ apply singleton_to_event
+ apply event_to_singleton at H1
+ apply event_t... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_d374244a6d7c_0 | 66290794f274a336 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Log.lean | Log | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 4 | [
{
"theorem_name": "galois_connection_ofReal",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [GaloisConnection]\n intro a b\n case_EReal_isENNReal a\n rename_i Hneg\n apply Iff.intro\n · intro _\n ... | [
{
"name": "ofEReal_eq_zero_iff",
"text": "lemma ofEReal_eq_zero_iff (w : EReal) : w ≤ 0 <-> ofEReal w = 0 := by\n apply Iff.intro\n · intro _\n case_EReal_isReal w\n · intro _\n case_EReal_isReal w\n\n",
"fan_in": 4,
"n_lines": 8,
"n_chars": 165,
"n_subproofs": 0,
"n_tactics": 6... | [
{
"name": "galois_connection_ofReal",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 17,
"n_chars": 388,
"n_subproofs": 0,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 10,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | @@ -185,6 +185,13 @@
@[simp]
lemma ofEReal_real (r : ℝ) : ofEReal r = ENNReal.ofReal r := by rfl
+lemma ofEReal_eq_zero_iff (w : EReal) : w ≤ 0 <-> ofEReal w = 0 := by
+ apply Iff.intro
+ · intro _
+ case_EReal_isReal w
+ · intro _
+ case_EReal_isReal w
+
@[simp]
lemma toEReal_ofENNReal_nonneg {w : EReal... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_d374244a6d7c_1 | 8650dc345ec6cf71 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Log.lean | Log | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "elog_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n all_goals case_ENNReal_isReal_zero x\n all_goals case_ENNReal_isReal_zero y\n rename_i r₁ Hr₁ HPr₁ r₂ Hr₂ HPr₂\n rw [← EReal.c... | [
{
"name": "elog_ENNReal_ofReal_of_pos",
"text": "lemma elog_ENNReal_ofReal_of_pos {x : ℝ} (H : 0 < x) : (ENNReal.ofReal x).elog = x.log.toEReal := by\n exact elog_of_pos_real H\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 131,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n... | [
{
"name": "elog_mul",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 16,
"n_chars": 431,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 4,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | @@ -279,8 +279,22 @@
simp [elog_of_pos_real (exp_pos v'), Real.log_exp]
· simp [eexp_top, elog_top]
+lemma elog_ENNReal_ofReal_of_pos {x : ℝ} (H : 0 < x) : (ENNReal.ofReal x).elog = x.log.toEReal := by
+ exact elog_of_pos_real H
+
@[simp]
-lemma elog_mul {x y : ENNReal} : elog x + elog y = elog (x * y) := s... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_d374244a6d7c_2 | b15fb4ea0de7b552 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Log.lean | Log | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "eexp_mono_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 28,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Iff.intro\n · intro H\n all_goals case_EReal_isReal w\n · apply bot_lt_iff_ne_bot.mpr\n apply bot_lt_iff_ne... | [
{
"name": "eexp_zero_iff",
"text": "lemma eexp_zero_iff {w : EReal} : eexp w = 0 <-> w = ⊥ := by\n apply Iff.intro\n · intro H\n all_goals case_EReal_isReal w\n rename_i r _\n have Hcont := exp_pos r\n linarith\n · simp_all\n\n\n",
"fan_in": 1,
"n_lines": 11,
"n_chars": 202,
"... | [
{
"name": "eexp_mono_lt",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 32,
"n_chars": 866,
"n_subproofs": 2,
"n_tactics": 28,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 19,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | @@ -312,18 +312,38 @@
rw [← exp_add]
rw [eexp_ofReal]
+lemma eexp_zero_iff {w : EReal} : eexp w = 0 <-> w = ⊥ := by
+ apply Iff.intro
+ · intro H
+ all_goals case_EReal_isReal w
+ rename_i r _
+ have Hcont := exp_pos r
+ linarith
+ · simp_all
+
lemma eexp_mono_lt {w z : EReal} : (w < z) <-> eexp... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_d374244a6d7c_3 | 49e95eb699969d82 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Log.lean | Log | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "eexp_mono_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 28,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Iff.intro\n · intro H\n all_goals case_EReal_isReal w\n · apply bot_lt_iff_ne_bot.mpr\n apply bot_lt_iff_ne... | [
{
"name": "eexp_zero_iff",
"text": "lemma eexp_zero_iff {w : EReal} : eexp w = 0 <-> w = ⊥ := by\n apply Iff.intro\n · intro H\n all_goals case_EReal_isReal w\n rename_i r _\n have Hcont := exp_pos r\n linarith\n · simp_all\n\n\n",
"fan_in": 1,
"n_lines": 11,
"n_chars": 202,
"... | [
{
"name": "eexp_mono_le",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 284,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesting": ... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | @@ -315,18 +315,38 @@
lemma eexp_injective {w z : EReal} : eexp w = eexp z -> w = z := by
intro H; have := congrArg elog H; simp at this; exact this
+lemma eexp_zero_iff {w : EReal} : eexp w = 0 <-> w = ⊥ := by
+ apply Iff.intro
+ · intro H
+ all_goals case_EReal_isReal w
+ rename_i r _
+ have Hcont :=... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_d374244a6d7c_4 | a9ed339a6de0ed07 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Log.lean | Log | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "elog_mono_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 21,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Iff.intro\n · intro H\n all_goals case_ENNReal_isReal_zero x\n · apply Ne.bot_lt'\n intro HK\n symm at... | [
{
"name": "elog_bot_iff",
"text": "lemma elog_bot_iff {x : ENNReal} : elog x = ⊥ <-> x = 0 := by\n apply Iff.intro\n · intro H\n all_goals case_ENNReal_isReal_zero x\n · simp_all\n\n\n\n",
"fan_in": 1,
"n_lines": 9,
"n_chars": 153,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic"... | [
{
"name": "elog_mono_lt",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 24,
"n_chars": 584,
"n_subproofs": 0,
"n_tactics": 22,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 10,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | @@ -312,11 +312,21 @@
rw [← exp_add]
rw [eexp_ofReal]
+lemma elog_bot_iff {x : ENNReal} : elog x = ⊥ <-> x = 0 := by
+ apply Iff.intro
+ · intro H
+ all_goals case_ENNReal_isReal_zero x
+ · simp_all
+
lemma elog_mono_lt {x y : ENNReal} : (x < y) <-> elog x < elog y := by
apply Iff.intro
· intro H
... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_d374244a6d7c_5 | 5ed2e39fa1c9642c | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Log.lean | Log | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "elog_mono_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 21,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Iff.intro\n · intro H\n all_goals case_ENNReal_isReal_zero x\n · apply Ne.bot_lt'\n intro HK\n symm at... | [
{
"name": "elog_bot_iff",
"text": "lemma elog_bot_iff {x : ENNReal} : elog x = ⊥ <-> x = 0 := by\n apply Iff.intro\n · intro H\n all_goals case_ENNReal_isReal_zero x\n · simp_all\n\n\n\n",
"fan_in": 1,
"n_lines": 9,
"n_chars": 153,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic"... | [
{
"name": "elog_mono_le",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 6,
"n_chars": 285,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesting": ... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | @@ -315,11 +315,21 @@
lemma elog_injective {x y : ENNReal} : elog x = elog y -> x = y := by
intro H; have := congrArg eexp H; simp at this; exact this
+lemma elog_bot_iff {x : ENNReal} : elog x = ⊥ <-> x = 0 := by
+ apply Iff.intro
+ · intro H
+ all_goals case_ENNReal_isReal_zero x
+ · simp_all
+
lemma elo... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_d374244a6d7c_6 | 94cb2542bc90b7bd | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Log.lean | Log | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "elog_mono_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 21,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Iff.intro\n · intro H\n all_goals case_ENNReal_isReal_zero x\n · apply Ne.bot_lt'\n intro HK\n symm at... | [
{
"name": "elog_bot_iff",
"text": "lemma elog_bot_iff {x : ENNReal} : elog x = ⊥ <-> x = 0 := by\n apply Iff.intro\n · intro H\n all_goals case_ENNReal_isReal_zero x\n · simp_all\n\n\n\n",
"fan_in": 1,
"n_lines": 9,
"n_chars": 153,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic"... | [
{
"name": "galois_connection_eexp",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 15,
"n_lines": 13,
"n_chars": 252,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 6,
"automation_only": false,
"m... | 8 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | @@ -327,6 +327,12 @@
linarith
· simp_all
+lemma elog_bot_iff {x : ENNReal} : elog x = ⊥ <-> x = 0 := by
+ apply Iff.intro
+ · intro H
+ all_goals case_ENNReal_isReal_zero x
+ · simp_all
+
lemma eexp_mono_lt {w z : EReal} : (w < z) <-> eexp w < eexp z := by
apply Iff.intro
· intro H
@@ -365,7 +371... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_d374244a6d7c_7 | 14927c3c0d9c8a18 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Log.lean | Log | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "ereal_smul_eq_left",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply LE.le.antisymm\n · apply ereal_smul_le_left s Hr1 Hr2 (le_of_eq H)\n · apply ereal_smul_le_left s Hr1 Hr2 (le_of... | [
{
"name": "ereal_smul_le_left",
"text": "lemma ereal_smul_le_left {w z : EReal} (s : EReal) (Hr1 : 0 < s) (Hr2 : s < ⊤) (H : s * w ≤ s * z) : w ≤ z := by\n cases s\n · exfalso\n simp at Hr1\n · rename_i s_R\n have Hsr : some (some s_R) = Real.toEReal s_R := rfl\n rw [<- Hsr] at H\n rw [<- Hsr... | [
{
"name": "ereal_smul_eq_left",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 260,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | @@ -316,10 +316,54 @@
section misc
+lemma ereal_smul_le_left {w z : EReal} (s : EReal) (Hr1 : 0 < s) (Hr2 : s < ⊤) (H : s * w ≤ s * z) : w ≤ z := by
+ cases s
+ · exfalso
+ simp at Hr1
+ · rename_i s_R
+ have Hsr : some (some s_R) = Real.toEReal s_R := rfl
+ rw [<- Hsr] at H
+ rw [<- Hsr] at Hr1
+ ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_d374244a6d7c_8 | f68de3f363be2c18 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Log.lean | Log | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "ereal_smul_eq_left",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply LE.le.antisymm\n · apply ereal_smul_le_left s Hr1 Hr2 (le_of_eq H)\n · apply ereal_smul_le_left s Hr1 Hr2 (le_of... | [
{
"name": "ereal_smul_le_left",
"text": "lemma ereal_smul_le_left {w z : EReal} (s : EReal) (Hr1 : 0 < s) (Hr2 : s < ⊤) (H : s * w ≤ s * z) : w ≤ z := by\n cases s\n · exfalso\n simp at Hr1\n · rename_i s_R\n have Hsr : some (some s_R) = Real.toEReal s_R := rfl\n rw [<- Hsr] at H\n rw [<- Hsr... | [
{
"name": "ereal_smul_lt_left",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 213,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | @@ -316,8 +316,55 @@
section misc
-lemma ereal_smul_lt_left {w z : EReal} (s : EReal) (Hr1 : 0 < s) (Hr2 : s < ⊤) (H : s * w < s * z) : w < z := sorry
+lemma ereal_smul_le_left {w z : EReal} (s : EReal) (Hr1 : 0 < s) (Hr2 : s < ⊤) (H : s * w ≤ s * z) : w ≤ z := by
+ cases s
+ · exfalso
+ simp at Hr1
+ · rena... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_d374244a6d7c_9 | 01bacd39588b4dea | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Log.lean | Log | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 4 | [
{
"theorem_name": "galois_connection_ofReal",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [GaloisConnection]\n intro a b\n case_EReal_isENNReal a\n rename_i Hneg\n apply Iff.intro\n · intro _\n ... | [
{
"name": "ofEReal_eq_zero_iff",
"text": "lemma ofEReal_eq_zero_iff (w : EReal) : w ≤ 0 <-> ofEReal w = 0 := by\n apply Iff.intro\n · intro _\n case_EReal_isReal w\n · intro _\n case_EReal_isReal w\n\n",
"fan_in": 4,
"n_lines": 8,
"n_chars": 165,
"n_subproofs": 0,
"n_tactics": 6... | [
{
"name": "ereal_smul_inv_cancel_1",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 19,
"n_chars": 537,
"n_subproofs": 0,
"n_tactics": 16,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 5,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | @@ -185,6 +185,13 @@
@[simp]
lemma ofEReal_real (r : ℝ) : ofEReal r = ENNReal.ofReal r := by rfl
+lemma ofEReal_eq_zero_iff (w : EReal) : w ≤ 0 <-> ofEReal w = 0 := by
+ apply Iff.intro
+ · intro _
+ case_EReal_isReal w
+ · intro _
+ case_EReal_isReal w
+
@[simp]
lemma toEReal_ofENNReal_nonneg {w : EReal... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_d374244a6d7c_10 | b4d4a5a6e0c1165d | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Log.lean | Log | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 4 | [
{
"theorem_name": "galois_connection_ofReal",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [GaloisConnection]\n intro a b\n case_EReal_isENNReal a\n rename_i Hneg\n apply Iff.intro\n · intro _\n ... | [
{
"name": "ofEReal_eq_zero_iff",
"text": "lemma ofEReal_eq_zero_iff (w : EReal) : w ≤ 0 <-> ofEReal w = 0 := by\n apply Iff.intro\n · intro _\n case_EReal_isReal w\n · intro _\n case_EReal_isReal w\n\n",
"fan_in": 4,
"n_lines": 8,
"n_chars": 165,
"n_subproofs": 0,
"n_tactics": 6... | [
{
"name": "ereal_smul_inv_cancel_2",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 22,
"n_chars": 591,
"n_subproofs": 0,
"n_tactics": 19,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 6,
"n_structural": 5,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | @@ -185,6 +185,13 @@
@[simp]
lemma ofEReal_real (r : ℝ) : ofEReal r = ENNReal.ofReal r := by rfl
+lemma ofEReal_eq_zero_iff (w : EReal) : w ≤ 0 <-> ofEReal w = 0 := by
+ apply Iff.intro
+ · intro _
+ case_EReal_isReal w
+ · intro _
+ case_EReal_isReal w
+
@[simp]
lemma toEReal_ofENNReal_nonneg {w : EReal... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_d374244a6d7c_11 | 73f0d1a3bccf35b2 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Log.lean | Log | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 4 | [
{
"theorem_name": "galois_connection_ofReal",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [GaloisConnection]\n intro a b\n case_EReal_isENNReal a\n rename_i Hneg\n apply Iff.intro\n · intro _\n ... | [
{
"name": "ofEReal_eq_zero_iff",
"text": "lemma ofEReal_eq_zero_iff (w : EReal) : w ≤ 0 <-> ofEReal w = 0 := by\n apply Iff.intro\n · intro _\n case_EReal_isReal w\n · intro _\n case_EReal_isReal w\n\n",
"fan_in": 4,
"n_lines": 8,
"n_chars": 165,
"n_subproofs": 0,
"n_tactics": 6... | [
{
"name": "galois_connection_smul_l",
"fan_in": 0,
"n_deps_direct": 6,
"n_deps_transitive": 6,
"n_lines": 34,
"n_chars": 952,
"n_subproofs": 1,
"n_tactics": 31,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 7,
"n_structural": 15,
"automation_only": false,
... | 5 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan, Markus de Medeiros
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.Data.EReal.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Basic
i... | @@ -185,6 +185,13 @@
@[simp]
lemma ofEReal_real (r : ℝ) : ofEReal r = ENNReal.ofReal r := by rfl
+lemma ofEReal_eq_zero_iff (w : EReal) : w ≤ 0 <-> ofEReal w = 0 := by
+ apply Iff.intro
+ · intro _
+ case_EReal_isReal w
+ · intro _
+ case_EReal_isReal w
+
/--
``ofEReal`` is injective for for positive ERe... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_395144f3257f_0 | cfb2cae099c4be19 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/GaussianGen/Properties.lean | Properties | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "DiscreteGaussianGenSample_apply",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have A : (num : ℝ) / (den : ℝ) ≠ 0 := by\n simp only [ne_eq, div_eq_zero_iff, cast_eq_zero, PNat.ne_zer... | [
{
"name": "if_simple_GaussianGen",
"text": "lemma if_simple_GaussianGen (x_1 x μ : ℤ) :\n (@ite ENNReal (x_1 = x - μ) (propDecidable (x_1 = x - μ)) 0\n (@ite ENNReal (x = x_1 + μ) (x.instDecidableEq (x_1 + μ))\n (ENNReal.ofReal (gauss_term_ℝ (↑↑num / ↑↑den) 0 ↑x_1 / ∑' (x : ℤ), gauss_term_ℝ (↑↑num / ↑↑de... | [
{
"name": "DiscreteGaussianGenSample_apply",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 23,
"n_chars": 760,
"n_subproofs": 1,
"n_tactics": 16,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 5,
"n_structural": 1,
"automation_only": false... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Samplers.GaussianGen.Code
import SampCert.Samplers.Gaussian.Properties
import SampCert.Util.Gaussian.DiscreteGaussian
impor... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Samplers.GaussianGen.Code
import SampCert.Samplers.Gaussian.Properties
import SampCert.Util.Gaussian.DiscreteGaussian
impor... | @@ -19,12 +19,39 @@
namespace SLang
+lemma if_simple_GaussianGen (x_1 x μ : ℤ) :
+ (@ite ENNReal (x_1 = x - μ) (propDecidable (x_1 = x - μ)) 0
+ (@ite ENNReal (x = x_1 + μ) (x.instDecidableEq (x_1 + μ))
+ (ENNReal.ofReal (gauss_term_ℝ (↑↑num / ↑↑den) 0 ↑x_1 / ∑' (x : ℤ), gauss_term_ℝ (↑↑num / ↑↑den) 0 ↑x)) 0)) ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_3d05c29cc4b0_0 | 31af4b4c502870ca | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Pure/Const.lean | Const | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "PureDP_privConst",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [PureDP] at *\n apply privConst_DP_Bound",
"n_chars": 51,
"n_subproofs": 0,
"n_tactics": 3,
"cycloma... | [
{
"name": "privConst_DP_Bound",
"text": "/--\nConstant query satisfies zCDP Renyi divergence bound.\n-/\ntheorem privConst_DP_Bound {u : U} : DP (privConst u : Mechanism T U) 0 := by\n rw [event_eq_singleton]\n rw [DP_singleton]\n intros\n simp [privConst]\n\n",
"fan_in": 1,
"n_lines": 10,
"... | [
{
"name": "PureDP_privConst",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 207,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.Pure.DP
/-!
# zCDP Constant function
This file proves a D... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.Pure.DP
/-!
# zCDP Constant function
This file proves a D... | @@ -21,9 +21,20 @@
variable { T U : Type }
/--
+Constant query satisfies zCDP Renyi divergence bound.
+-/
+theorem privConst_DP_Bound {u : U} : DP (privConst u : Mechanism T U) 0 := by
+ rw [event_eq_singleton]
+ rw [DP_singleton]
+ intros
+ simp [privConst]
+
+/--
``privComposeAdaptive`` satisfies zCDP
-/
-t... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_94dbd4b81eeb_0 | ff228d6a20222e27 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/UnboundedMax/Code.lean | Code | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "exactDiffSum_append",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [exactDiffSum]\n rw [exactClippedSum_append]\n rw [exactClippedSum_append]\n linarith",
"n_chars": 96,
... | [
{
"name": "exactClippedSum_append",
"text": "lemma exactClippedSum_append : exactClippedSum i (A ++ B) = exactClippedSum i A + exactClippedSum i B := by\n simp [exactClippedSum]\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 134,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"... | [
{
"name": "exactDiffSum_append",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 289,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Pure.System
import SampCert.DifferentialPrivacy.Queries.Abov... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Pure.System
import SampCert.DifferentialPrivacy.Queries.Abov... | @@ -56,8 +56,15 @@
· linarith
· linarith
-lemma exactDiffSum_append : exactDiffSum i (A ++ B) = exactDiffSum i A + exactDiffSum i B := sorry
+lemma exactClippedSum_append : exactClippedSum i (A ++ B) = exactClippedSum i A + exactClippedSum i B := by
+ simp [exactClippedSum]
+lemma exactDiffSum_append : e... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_94dbd4b81eeb_1 | 0830b55292f40ace | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/UnboundedMax/Code.lean | Code | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "lucky_guess",
"depth": 1,
"n_commands": 0,
"n_lines": 35,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros τ l\n exists (List.length l + τ)\n intro A K' HK'\n apply ge_iff_le.mpr\n apply le_trans _ ?G1\n case G1 =>\n a... | [
{
"name": "exactDiffSum_singleton_le_1",
"text": "lemma exactDiffSum_singleton_le_1 : -1 ≤ exactDiffSum point [v] := by\n simp [exactDiffSum, exactClippedSum]\n cases (Classical.em (point ≤ v))\n · right\n trivial\n · left\n rename_i h\n simp at h\n rw [Int.min_def]\n simp\n split\n ... | [
{
"name": "lucky_guess",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 37,
"n_chars": 716,
"n_subproofs": 1,
"n_tactics": 34,
"cyclomatic": 4,
"n_automation": 5,
"n_rewrites": 12,
"n_structural": 10,
"automation_only": false,
"max_nesting... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Pure.System
import SampCert.DifferentialPrivacy.Queries.Abov... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Pure.System
import SampCert.DifferentialPrivacy.Queries.Abov... | @@ -42,6 +42,20 @@
simp
-/
+lemma exactDiffSum_singleton_le_1 : -1 ≤ exactDiffSum point [v] := by
+ simp [exactDiffSum, exactClippedSum]
+ cases (Classical.em (point ≤ v))
+ · right
+ trivial
+ · left
+ rename_i h
+ simp at h
+ rw [Int.min_def]
+ simp
+ split
+ · linarith
+ · linarit... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_56149afb47e2_0 | bd7ccf36ca639922 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/DiscreteGaussian.lean | DiscreteGaussian | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "summable_gauss_term",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [gauss_term_jacobi]\n apply Summable.mul_right\n rw [summable_jacobiTheta₂_term_iff]\n apply jacobi_tau_positive ... | [
{
"name": "jacobi_tau_positive",
"text": "lemma jacobi_tau_positive {σ : ℝ} (h : σ ≠ 0) :\n 0 < (Complex.I * ((2 : ℂ) * σ^2)⁻¹ * π⁻¹).im := by\n simp [pi_pos, h, sq]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 141,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automatio... | [
{
"name": "summable_gauss_term",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 13,
"n_chars": 365,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_ne... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | @@ -89,13 +89,21 @@
simp [pi_ne_zero]
ring_nf
+lemma jacobi_tau_positive {σ : ℝ} (h : σ ≠ 0) :
+ 0 < (Complex.I * ((2 : ℂ) * σ^2)⁻¹ * π⁻¹).im := by
+ simp [pi_pos, h, sq]
+
/--
``gauss_term_ℂ`` is summable over ℤ.
Proven by specializing the summability from the Jacobi Theta function.
-/
theorem summabl... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_56149afb47e2_1 | 55b2cea01c742f80 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/DiscreteGaussian.lean | DiscreteGaussian | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "asymptotics_fourier_gauss_term",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [fourier_gauss_term_correspondance h]\n apply IsLittleO.isBigO\n unfold fourier_gauss_term\n conv =>\... | [
{
"name": "fourier_gauss_term_correspondance",
"text": "/--\n``fourier_gauss_term`` is the Fourier transform of the ``gauss_term`` with mean 0.\n-/\ntheorem fourier_gauss_term_correspondance {σ : ℝ} (h : σ ≠ 0) :\n (𝓕 ((gauss_term_ℂ σ 0 : ℝ → ℂ))) = fourier_gauss_term σ := by\n have P : 0 < (π * (2 : ℂ) ... | [
{
"name": "asymptotics_fourier_gauss_term",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 30,
"n_chars": 832,
"n_subproofs": 3,
"n_tactics": 23,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 7,
"n_structural": 5,
"automation_only": false,... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | @@ -118,11 +118,57 @@
apply summable_gauss_term h
/--
+``fourier_gauss_term`` is the Fourier transform of the ``gauss_term`` with mean 0.
+-/
+theorem fourier_gauss_term_correspondance {σ : ℝ} (h : σ ≠ 0) :
+ (𝓕 ((gauss_term_ℂ σ 0 : ℝ → ℂ))) = fourier_gauss_term σ := by
+ have P : 0 < (π * (2 : ℂ) * σ^2)⁻¹.re ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_56149afb47e2_2 | 167e47c09aa90293 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/DiscreteGaussian.lean | DiscreteGaussian | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "poisson_gauss_term",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have B := asymptotics_gauss_term h\n have C := asymptotics_fourier_gauss_term h\n have D : (1 : ℝ) < 2 := one_lt_two\n... | [
{
"name": "asymptotics_fourier_gauss_term",
"text": "/--\nBig O asymptotic for Fourier transform of ``gauss_term``.\n-/\ntheorem asymptotics_fourier_gauss_term {σ : ℝ} (h : σ ≠ 0) :\n (𝓕 ((gauss_term_ℂ σ 0 : ℝ → ℂ))) =O[cocompact ℝ] (fun x => |x| ^ (-2 : ℝ)) := by\n rw [fourier_gauss_term_correspondance ... | [
{
"name": "poisson_gauss_term",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 13,
"n_chars": 542,
"n_subproofs": 4,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nes... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | @@ -165,10 +165,45 @@
simp
/--
+Big O asymptotic for Fourier transform of ``gauss_term``.
+-/
+theorem asymptotics_fourier_gauss_term {σ : ℝ} (h : σ ≠ 0) :
+ (𝓕 ((gauss_term_ℂ σ 0 : ℝ → ℂ))) =O[cocompact ℝ] (fun x => |x| ^ (-2 : ℝ)) := by
+ rw [fourier_gauss_term_correspondance h]
+ apply IsLittleO.isBigO
+ ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_56149afb47e2_3 | ee8ea6e2980f3c44 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/DiscreteGaussian.lean | DiscreteGaussian | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "poisson_gauss_term",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have B := asymptotics_gauss_term h\n have C := asymptotics_fourier_gauss_term h\n have D : (1 : ℝ) < 2 := one_lt_two\n... | [
{
"name": "asymptotics_fourier_gauss_term",
"text": "/--\nBig O asymptotic for Fourier transform of ``gauss_term``.\n-/\ntheorem asymptotics_fourier_gauss_term {σ : ℝ} (h : σ ≠ 0) :\n (𝓕 ((gauss_term_ℂ σ 0 : ℝ → ℂ))) =O[cocompact ℝ] (fun x => |x| ^ (-2 : ℝ)) := by\n rw [fourier_gauss_term_correspondance ... | [
{
"name": "summable_fourier_gauss_term",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 649,
"n_subproofs": 3,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | @@ -141,10 +141,43 @@
simp
/--
+Big O asymptotic for Fourier transform of ``gauss_term``.
+-/
+theorem asymptotics_fourier_gauss_term {σ : ℝ} (h : σ ≠ 0) :
+ (𝓕 ((gauss_term_ℂ σ 0 : ℝ → ℂ))) =O[cocompact ℝ] (fun x => |x| ^ (-2 : ℝ)) := by
+ rw [fourier_gauss_term_correspondance h]
+ apply IsLittleO.isBigO
+ ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_56149afb47e2_4 | 2595224afabc7cbd | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/DiscreteGaussian.lean | DiscreteGaussian | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "poisson_gauss_term",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have B := asymptotics_gauss_term h\n have C := asymptotics_fourier_gauss_term h\n have D : (1 : ℝ) < 2 := one_lt_two\n... | [
{
"name": "asymptotics_gauss_term",
"text": "/--\nBig O asymptotic for ``gauss_term``.\n-/\ntheorem asymptotics_gauss_term {σ : ℝ} (h : σ ≠ 0) :\n gauss_term_ℂ σ 0 =O[cocompact ℝ] (fun x => |x| ^ (-2 : ℝ)) := by\n apply IsLittleO.isBigO\n unfold gauss_term_ℂ gauss_term_ℝ\n simp only [ContinuousMap.coe_m... | [
{
"name": "fourier_coeff_correspondance",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 610,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | @@ -118,10 +118,38 @@
apply summable_gauss_term h
/--
+Big O asymptotic for ``gauss_term``.
+-/
+theorem asymptotics_gauss_term {σ : ℝ} (h : σ ≠ 0) :
+ gauss_term_ℂ σ 0 =O[cocompact ℝ] (fun x => |x| ^ (-2 : ℝ)) := by
+ apply IsLittleO.isBigO
+ unfold gauss_term_ℂ gauss_term_ℝ
+ simp only [ContinuousMap.coe_mk... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_56149afb47e2_5 | 6143bc81f0952379 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/DiscreteGaussian.lean | DiscreteGaussian | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "poisson_gauss_term",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have B := asymptotics_gauss_term h\n have C := asymptotics_fourier_gauss_term h\n have D : (1 : ℝ) < 2 := one_lt_two\n... | [
{
"name": "asymptotics_fourier_gauss_term",
"text": "/--\nBig O asymptotic for Fourier transform of ``gauss_term``.\n-/\ntheorem asymptotics_fourier_gauss_term {σ : ℝ} (h : σ ≠ 0) :\n (𝓕 ((gauss_term_ℂ σ 0 : ℝ → ℂ))) =O[cocompact ℝ] (fun x => |x| ^ (-2 : ℝ)) := by\n rw [fourier_gauss_term_correspondance ... | [
{
"name": "summable_fourier_gauss_term'",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 20,
"n_chars": 688,
"n_subproofs": 2,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 4,
"n_structural": 4,
"automation_only": false,
... | 5 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | @@ -165,10 +165,43 @@
simp
/--
+Big O asymptotic for Fourier transform of ``gauss_term``.
+-/
+theorem asymptotics_fourier_gauss_term {σ : ℝ} (h : σ ≠ 0) :
+ (𝓕 ((gauss_term_ℂ σ 0 : ℝ → ℂ))) =O[cocompact ℝ] (fun x => |x| ^ (-2 : ℝ)) := by
+ rw [fourier_gauss_term_correspondance h]
+ apply IsLittleO.isBigO
+ ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_56149afb47e2_6 | a48acda35f2588f5 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/DiscreteGaussian.lean | DiscreteGaussian | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 3 | [
{
"theorem_name": "gauss_term_noneg",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold gauss_term_ℝ\n apply le_of_lt (gauss_term_pos σ μ n)",
"n_chars": 69,
"n_subproofs": 0,
"n_tactics": 3... | [
{
"name": "gauss_term_pos",
"text": "lemma gauss_term_pos (σ μ : ℝ) (n : ℤ) :\n 0 < (gauss_term_ℝ σ μ) n := by\n unfold gauss_term_ℝ\n apply exp_pos\n\n",
"fan_in": 3,
"n_lines": 6,
"n_chars": 125,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_re... | [
{
"name": "gauss_term_noneg",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 155,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | @@ -117,8 +117,15 @@
rw [← gauss_term_swap]
apply summable_gauss_term h
+lemma gauss_term_pos (σ μ : ℝ) (n : ℤ) :
+ 0 < (gauss_term_ℝ σ μ) n := by
+ unfold gauss_term_ℝ
+ apply exp_pos
+
lemma gauss_term_noneg (σ μ : ℝ) (n : ℤ) :
- 0 ≤ (gauss_term_ℝ σ μ) n := sorry
+ 0 ≤ (gauss_term_ℝ σ μ) n := by
+ un... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_56149afb47e2_7 | 15d88e6e15721a56 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/DiscreteGaussian.lean | DiscreteGaussian | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 3 | [
{
"theorem_name": "gauss_term_noneg",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold gauss_term_ℝ\n apply le_of_lt (gauss_term_pos σ μ n)",
"n_chars": 69,
"n_subproofs": 0,
"n_tactics": 3... | [
{
"name": "gauss_term_pos",
"text": "lemma gauss_term_pos (σ μ : ℝ) (n : ℤ) :\n 0 < (gauss_term_ℝ σ μ) n := by\n unfold gauss_term_ℝ\n apply exp_pos\n\n",
"fan_in": 3,
"n_lines": 6,
"n_chars": 125,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_re... | [
{
"name": "sum_gauss_term_nonneg",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 8,
"n_lines": 8,
"n_chars": 223,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_n... | 8 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | @@ -117,8 +117,15 @@
rw [← gauss_term_swap]
apply summable_gauss_term h
+lemma gauss_term_pos (σ μ : ℝ) (n : ℤ) :
+ 0 < (gauss_term_ℝ σ μ) n := by
+ unfold gauss_term_ℝ
+ apply exp_pos
+
lemma gauss_term_noneg (σ μ : ℝ) (n : ℤ) :
- 0 ≤ (gauss_term_ℝ σ μ) n := sorry
+ 0 ≤ (gauss_term_ℝ σ μ) n := by
+ un... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_56149afb47e2_8 | 2d27c7f9a643090a | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/DiscreteGaussian.lean | DiscreteGaussian | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "sum_gauss_term_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (summable_gauss_term' h μ).tsum_pos _ 0\n · apply gauss_term_pos\n · intro i\n apply gauss_term_noneg",
"... | [
{
"name": "gauss_term_noneg",
"text": "lemma gauss_term_noneg (σ μ : ℝ) (n : ℤ) :\n 0 ≤ (gauss_term_ℝ σ μ) n := by\n unfold gauss_term_ℝ\n apply le_of_lt (gauss_term_pos σ μ n)\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 155,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
... | [
{
"name": "discrete_gaussian_nonneg",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 9,
"n_lines": 8,
"n_chars": 216,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"ma... | 9 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | @@ -122,6 +122,11 @@
unfold gauss_term_ℝ
apply exp_pos
+lemma gauss_term_noneg (σ μ : ℝ) (n : ℤ) :
+ 0 ≤ (gauss_term_ℝ σ μ) n := by
+ unfold gauss_term_ℝ
+ apply le_of_lt (gauss_term_pos σ μ n)
+
/--
The sum of ``gauss_term_ℝ`` is positive.
-/
@@ -129,7 +134,8 @@
0 < (∑' (x : ℤ), (gauss_term_ℝ σ μ) x) ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_56149afb47e2_9 | 7c67fc5ff9433e6d | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/DiscreteGaussian.lean | DiscreteGaussian | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 3 | [
{
"theorem_name": "sum_gauss_term_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (summable_gauss_term' h μ).tsum_pos _ 0\n · apply gauss_term_pos\n · intro i\n apply gauss_term_noneg",
"... | [
{
"name": "summable_gauss_term'",
"text": "/--\n``gauss_term_ℝ`` is summable over ℝ.\n-/\ntheorem summable_gauss_term' {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) :\n Summable fun n : ℤ => gauss_term_ℝ σ μ n := by\n rw [← Complex.summable_ofReal]\n conv =>\n arg 1\n intro n\n rw [← gauss_term_swap]\n apply sum... | [
{
"name": "discrete_gaussian_summable",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 10,
"n_chars": 265,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
... | 5 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | @@ -105,6 +105,18 @@
rw [summable_jacobiTheta₂_term_iff]
apply jacobi_tau_positive h
+/--
+``gauss_term_ℝ`` is summable over ℝ.
+-/
+theorem summable_gauss_term' {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) :
+ Summable fun n : ℤ => gauss_term_ℝ σ μ n := by
+ rw [← Complex.summable_ofReal]
+ conv =>
+ arg 1
+ intro n
+... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_56149afb47e2_10 | 344f68210599d922 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Gaussian/DiscreteGaussian.lean | DiscreteGaussian | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 3 | [
{
"theorem_name": "sum_gauss_term_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (summable_gauss_term' h μ).tsum_pos _ 0\n · apply gauss_term_pos\n · intro i\n apply gauss_term_noneg",
"... | [
{
"name": "summable_gauss_term'",
"text": "/--\n``gauss_term_ℝ`` is summable over ℝ.\n-/\ntheorem summable_gauss_term' {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) :\n Summable fun n : ℤ => gauss_term_ℝ σ μ n := by\n rw [← Complex.summable_ofReal]\n conv =>\n arg 1\n intro n\n rw [← gauss_term_swap]\n apply sum... | [
{
"name": "discrete_gaussian_summable'",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 10,
"n_chars": 263,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
... | 5 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Discrete G... | @@ -105,6 +105,18 @@
rw [summable_jacobiTheta₂_term_iff]
apply jacobi_tau_positive h
+/--
+``gauss_term_ℝ`` is summable over ℝ.
+-/
+theorem summable_gauss_term' {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) :
+ Summable fun n : ℤ => gauss_term_ℝ σ μ n := by
+ rw [← Complex.summable_ofReal]
+ conv =>
+ arg 1
+ intro n
+... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_628d80dbf5f9_0 | a326ee7e5161f494 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Privacy.lean | Privacy | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "laplace_inequality",
"depth": 1,
"n_commands": 0,
"n_lines": 23,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply le_trans _ ?G1\n case G1 =>\n apply mul_le_mul_right\n apply laplace_inequality'\n repeat rw [<... | [
{
"name": "laplace_inequality'",
"text": "lemma laplace_inequality' (τ τ' : ℤ) (Δ : ℕ+) :\n ((ENNReal.ofReal (Real.exp (-abs τ' / (Δ * ε₂ / ε₁)))) * ((DiscreteLaplaceGenSamplePMF (Δ * ε₂) ε₁ 0 τ))) ≤\n (DiscreteLaplaceGenSamplePMF (Δ * ε₂) ε₁ 0) (τ + τ') := by\n simp [DiscreteLaplaceGenSamplePMF,... | [
{
"name": "laplace_inequality",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 29,
"n_chars": 770,
"n_subproofs": 0,
"n_tactics": 23,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 7,
"n_structural": 8,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Properties
import SampCert.DifferentialP... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Properties
import SampCert.DifferentialP... | @@ -22,9 +22,69 @@
-- exactDiffSum (point + 1) l₂ - exactDiffSum (point + 1) l₁ + cov_τ_def qs v0 vs l₁ l₂
qs (point + 1) l₂ - qs (point + 1) l₁ + cov_τ_def qs v0 vs l₁ l₂
+lemma laplace_inequality' (τ τ' : ℤ) (Δ : ℕ+) :
+ ((ENNReal.ofReal (Real.exp (-abs τ' / (Δ * ε₂ / ε₁)))) * ((DiscreteLaplaceGenSampleP... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_628d80dbf5f9_1 | 68635263df97c07e | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Privacy.lean | Privacy | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "laplace_inequality",
"depth": 1,
"n_commands": 0,
"n_lines": 23,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply le_trans _ ?G1\n case G1 =>\n apply mul_le_mul_right\n apply laplace_inequality'\n repeat rw [<... | [
{
"name": "laplace_inequality'",
"text": "lemma laplace_inequality' (τ τ' : ℤ) (Δ : ℕ+) :\n ((ENNReal.ofReal (Real.exp (-abs τ' / (Δ * ε₂ / ε₁)))) * ((DiscreteLaplaceGenSamplePMF (Δ * ε₂) ε₁ 0 τ))) ≤\n (DiscreteLaplaceGenSamplePMF (Δ * ε₂) ε₁ 0) (τ + τ') := by\n simp [DiscreteLaplaceGenSamplePMF,... | [
{
"name": "laplace_inequality_sub",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 10,
"n_chars": 379,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Properties
import SampCert.DifferentialP... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Properties
import SampCert.DifferentialP... | @@ -22,10 +22,70 @@
-- exactDiffSum (point + 1) l₂ - exactDiffSum (point + 1) l₁ + cov_τ_def qs v0 vs l₁ l₂
qs (point + 1) l₂ - qs (point + 1) l₁ + cov_τ_def qs v0 vs l₁ l₂
+lemma laplace_inequality' (τ τ' : ℤ) (Δ : ℕ+) :
+ ((ENNReal.ofReal (Real.exp (-abs τ' / (Δ * ε₂ / ε₁)))) * ((DiscreteLaplaceGenSample... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_628d80dbf5f9_2 | 50a3462cd67c8289 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Privacy.lean | Privacy | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "Hsens_cov_τ_lemma",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [sv8_sum]\n rw [add_tsub_add_eq_tsub_right]\n have X := @DSN sv_T qs l₁ l₂ Hqs_sens H.length HN\n rw [← Int... | [
{
"name": "DSN",
"text": "lemma DSN (Hqs_sens : ∀ i, sensitivity (qs i) 1) (N : ℕ) (H : Neighbour L1 L2) : ((qs N L1) : ℝ) - (qs N L2) ≤ 1 := by\n let Hqs_sens' := Hqs_sens N L1 L2 H\n rw [← Int.cast_sub]\n rw [<- Int.cast_one]\n apply Int.cast_le.mpr\n let X1 := Int.ofNat_le_ofNat_of_le Hqs_sens'\n s... | [
{
"name": "Hsens_cov_τ_lemma",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 585,
"n_subproofs": 2,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Properties
import SampCert.DifferentialP... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Properties
import SampCert.DifferentialP... | @@ -22,6 +22,26 @@
-- exactDiffSum (point + 1) l₂ - exactDiffSum (point + 1) l₁ + cov_τ_def qs v0 vs l₁ l₂
qs (point + 1) l₂ - qs (point + 1) l₁ + cov_τ_def qs v0 vs l₁ l₂
-lemma Hsens_cov_τ_lemma (Hqs_sens : ∀ i, sensitivity (qs i) 1) (HN : Neighbour l₁ l₂) : sv8_sum qs l₁ H v0 - sv8_sum qs l₂ H v0 ≤ OfNat.ofN... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_628d80dbf5f9_3 | bb3b828849f57b6c | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Privacy.lean | Privacy | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "Hsens_cov_τ_lemma",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [sv8_sum]\n rw [add_tsub_add_eq_tsub_right]\n have X := @DSN sv_T qs l₁ l₂ Hqs_sens H.length HN\n rw [← Int... | [
{
"name": "DSN",
"text": "lemma DSN (Hqs_sens : ∀ i, sensitivity (qs i) 1) (N : ℕ) (H : Neighbour L1 L2) : ((qs N L1) : ℝ) - (qs N L2) ≤ 1 := by\n let Hqs_sens' := Hqs_sens N L1 L2 H\n rw [← Int.cast_sub]\n rw [<- Int.cast_one]\n apply Int.cast_le.mpr\n let X1 := Int.ofNat_le_ofNat_of_le Hqs_sens'\n s... | [
{
"name": "Hsens_cov_τ",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 23,
"n_chars": 742,
"n_subproofs": 1,
"n_tactics": 19,
"cyclomatic": 4,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 10,
"automation_only": false,
"max_nesting"... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Properties
import SampCert.DifferentialP... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Properties
import SampCert.DifferentialP... | @@ -22,8 +22,28 @@
-- exactDiffSum (point + 1) l₂ - exactDiffSum (point + 1) l₁ + cov_τ_def qs v0 vs l₁ l₂
qs (point + 1) l₂ - qs (point + 1) l₁ + cov_τ_def qs v0 vs l₁ l₂
-lemma Hsens_cov_τ_lemma (Hqs_sens : ∀ i, sensitivity (qs i) 1) (HN : Neighbour l₁ l₂) : sv8_sum qs l₁ H v0 - sv8_sum qs l₂ H v0 ≤ OfNat.ofN... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_628d80dbf5f9_4 | 778ca895c229f580 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/AboveThresh/Privacy.lean | Privacy | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "Hsens_cov_τ_lemma",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [sv8_sum]\n rw [add_tsub_add_eq_tsub_right]\n have X := @DSN sv_T qs l₁ l₂ Hqs_sens H.length HN\n rw [← Int... | [
{
"name": "DSN",
"text": "lemma DSN (Hqs_sens : ∀ i, sensitivity (qs i) 1) (N : ℕ) (H : Neighbour L1 L2) : ((qs N L1) : ℝ) - (qs N L2) ≤ 1 := by\n let Hqs_sens' := Hqs_sens N L1 L2 H\n rw [← Int.cast_sub]\n rw [<- Int.cast_one]\n apply Int.cast_le.mpr\n let X1 := Int.ofNat_le_ofNat_of_le Hqs_sens'\n s... | [
{
"name": "Hsens_cov_vk",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 14,
"n_chars": 625,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_nesting"... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Properties
import SampCert.DifferentialP... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Queries.AboveThresh.Properties
import SampCert.DifferentialP... | @@ -22,8 +22,28 @@
-- exactDiffSum (point + 1) l₂ - exactDiffSum (point + 1) l₁ + cov_τ_def qs v0 vs l₁ l₂
qs (point + 1) l₂ - qs (point + 1) l₁ + cov_τ_def qs v0 vs l₁ l₂
-lemma Hsens_cov_τ_lemma (Hqs_sens : ∀ i, sensitivity (qs i) 1) (HN : Neighbour l₁ l₂) : sv8_sum qs l₁ H v0 - sv8_sum qs l₂ H v0 ≤ OfNat.ofN... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8c681a17216d_0 | 161b5bb8384b4780 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/Sparse/Privacy.lean | Privacy | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "privSparseAux_DP",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction c\n · intro _ _\n unfold privSparseAux\n simp\n apply dps.const_prop\n simp_all\n · rename_i c' I... | [
{
"name": "shift_qs_add",
"text": "lemma shift_qs_add {T : Type} (qs' : sv_query T) (A B : ℕ) : (shift_qs A (shift_qs B qs')) = (shift_qs (A + B) qs') := by\n apply funext; simp [shift_qs, add_assoc]\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 168,
"n_subproofs": 0,
"n_tactics": 3,
... | [
{
"name": "privSparseAux_DP",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 24,
"n_chars": 725,
"n_subproofs": 0,
"n_tactics": 19,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 9,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Pure.System
import SampCert.DifferentialPrivacy.Queries.Spar... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Pure.System
import SampCert.DifferentialPrivacy.Queries.Spar... | @@ -22,6 +22,9 @@
variable (qs : sv_query sv_T)
+lemma shift_qs_add {T : Type} (qs' : sv_query T) (A B : ℕ) : (shift_qs A (shift_qs B qs')) = (shift_qs (A + B) qs') := by
+ apply funext; simp [shift_qs, add_assoc]
+
local instance : MeasurableSpace (List ℕ) := ⊤
local instance : DiscreteMeasurableSpace (List ℕ)... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8c681a17216d_1 | 59f771bf0732dd9f | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/Sparse/Privacy.lean | Privacy | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "privSparse_DP",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold privSparse\n apply privSparseAux_DP (HDP := HDP)\n trivial",
"n_chars": 71,
"n_subproofs": 0,
"n_tactics... | [
{
"name": "privSparseAux_DP",
"text": "lemma privSparseAux_DP\n (HDP : ∀ N H, ∀ ε : NNReal, (ε = ε₁ / ε₂) -> dps.prop (sv1_aboveThresh_PMF (shift_qs N qs) T H ε₁ ε₂) ε)\n (ε : NNReal) (c : ℕ) (Hε : ε = ε₁ / ε₂) :\n ∀ N : ℕ, ∀ H, dps.prop (privSparseAux T ε₁ ε₂ (shift_qs N qs) H c) (c * ε) := by\n ... | [
{
"name": "privSparse_DP",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 360,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Pure.System
import SampCert.DifferentialPrivacy.Queries.Spar... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus de Medeiros
-/
import SampCert.DifferentialPrivacy.Abstract
import SampCert.DifferentialPrivacy.Pure.System
import SampCert.DifferentialPrivacy.Queries.Spar... | @@ -29,8 +29,34 @@
local instance : DiscreteMeasurableSpace (List ℕ) where
forall_measurableSet _ := .congr trivial rfl
+lemma privSparseAux_DP
+ (HDP : ∀ N H, ∀ ε : NNReal, (ε = ε₁ / ε₂) -> dps.prop (sv1_aboveThresh_PMF (shift_qs N qs) T H ε₁ ε₂) ε)
+ (ε : NNReal) (c : ℕ) (Hε : ε = ε₁ / ε₂) :
+ ∀ N : ℕ,... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_22617216f256_0 | 2a374933b85fe378 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Util/Shift.lean | Shift | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "tsum_shift",
"depth": 1,
"n_commands": 0,
"n_lines": 36,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h : ∀ μ : ℤ, Summable fun x : ℕ => f (x + μ) := by\n intro μ\n have A := @summable_int_iff_summable_nat_and_neg_add_... | [
{
"name": "tsum_shift₁",
"text": "/--\nA series is right-ℕ-shift-invariant provided its shifted positive and negative parts are summable.\n-/\ntheorem tsum_shift₁ (f : ℤ → ℝ) (μ : ℕ)\n (h2 : ∀ μ : ℕ, Summable fun x : ℕ => f (x + μ))\n (h3 : ∀ μ : ℕ, Summable fun x : ℕ => f (-(x + 1) + μ))\n :\n (∑' x : ... | [
{
"name": "tsum_shift",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 42,
"n_chars": 1339,
"n_subproofs": 8,
"n_tactics": 36,
"cyclomatic": 4,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 17,
"automation_only": false,
"max_nesting"... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
/-!
# Shift Util
This ... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
/-!
# Shift Util
This ... | @@ -15,6 +15,52 @@
open Summable
/--
+A series is right-ℕ-shift-invariant provided its shifted positive and negative parts are summable.
+-/
+theorem tsum_shift₁ (f : ℤ → ℝ) (μ : ℕ)
+ (h2 : ∀ μ : ℕ, Summable fun x : ℕ => f (x + μ))
+ (h3 : ∀ μ : ℕ, Summable fun x : ℕ => f (-(x + 1) + μ))
+ :
+ (∑' x : ℤ, f x) =... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_0b6e05ecd739_0 | 0a4b5fc9bc32e099 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Bernoulli/Properties.lean | Properties | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "BernoulliSample_normalizes'",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← tsum_fintype (L := .unconditional _)]\n apply BernoulliSample_normalizes num den wf",
"n_chars": 97,... | [
{
"name": "BernoulliSample_normalizes",
"text": "/--\nTotal mass of the Bernoulli sampler is 1.\n-/\n@[simp]\ntheorem BernoulliSample_normalizes (num : Nat) (den : PNat) (wf : num ≤ den) :\n ∑' b : Bool, BernoulliSample num den wf b = 1 := by\n simp [BernoulliSample]\n rw [← ENNReal.tsum_add]\n have hEq... | [
{
"name": "BernoulliSample_normalizes'",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 281,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import Mathlib.Probability.Distributions.Uniform
import SampCert.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import Mathlib.Probability.Distributions.Uniform
import SampCert.S... | @@ -23,8 +23,27 @@
/--
Total mass of the Bernoulli sampler is 1.
-/
+@[simp]
+theorem BernoulliSample_normalizes (num : Nat) (den : PNat) (wf : num ≤ den) :
+ ∑' b : Bool, BernoulliSample num den wf b = 1 := by
+ simp [BernoulliSample]
+ rw [← ENNReal.tsum_add]
+ have hEq : ∀ a : ℕ, (if a < num then UniformSampl... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_fa5a88b92d24_0 | bd276af7e810922a | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/Histogram/Properties.lean | Properties | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "privNoisedBinCount_DP",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold privNoisedBinCount\n apply dpn.noise_prop HN_bin\n apply exactBinCount_sensitivity",
"n_chars": 95,
... | [
{
"name": "exactBinCount_sensitivity",
"text": "theorem exactBinCount_sensitivity (b : Fin numBins) : sensitivity (exactBinCount numBins B b) 1 := by\n rw [sensitivity]\n intros _ _ H\n cases H\n all_goals simp_all [exactBinCount, exactBinCount, List.filter_cons]\n all_goals aesop\n\n",
"fan_in": 1... | [
{
"name": "privNoisedBinCount_DP",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 328,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Queries.Histogram.Code
import SampCert.DifferentialPrivacy.Sensitivity
import SampCert.DifferentialPriv... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Queries.Histogram.Code
import SampCert.DifferentialPrivacy.Sensitivity
import SampCert.DifferentialPriv... | @@ -26,6 +26,13 @@
/-
exactBinCount is 1-sensitive
-/
+theorem exactBinCount_sensitivity (b : Fin numBins) : sensitivity (exactBinCount numBins B b) 1 := by
+ rw [sensitivity]
+ intros _ _ H
+ cases H
+ all_goals simp_all [exactBinCount, exactBinCount, List.filter_cons]
+ all_goals aesop
+
section DPBounds
... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_fa5a88b92d24_1 | a86e85638115d691 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/Histogram/Properties.lean | Properties | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "privNoisedBinCount_DP",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold privNoisedBinCount\n apply dpn.noise_prop HN_bin\n apply exactBinCount_sensitivity",
"n_chars": 95,
... | [
{
"name": "exactBinCount_sensitivity",
"text": "theorem exactBinCount_sensitivity (b : Fin numBins) : sensitivity (exactBinCount numBins B b) 1 := by\n rw [sensitivity]\n intros _ _ H\n cases H\n all_goals simp_all [exactBinCount, exactBinCount, List.filter_cons]\n all_goals aesop\n\n",
"fan_in": 1... | [
{
"name": "privNoisedHistogramAux_DP",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 22,
"n_chars": 735,
"n_subproofs": 0,
"n_tactics": 19,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 11,
"automation_only": false,
... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Queries.Histogram.Code
import SampCert.DifferentialPrivacy.Sensitivity
import SampCert.DifferentialPriv... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Queries.Histogram.Code
import SampCert.DifferentialPrivacy.Sensitivity
import SampCert.DifferentialPriv... | @@ -26,6 +26,13 @@
/-
exactBinCount is 1-sensitive
-/
+theorem exactBinCount_sensitivity (b : Fin numBins) : sensitivity (exactBinCount numBins B b) 1 := by
+ rw [sensitivity]
+ intros _ _ H
+ cases H
+ all_goals simp_all [exactBinCount, exactBinCount, List.filter_cons]
+ all_goals aesop
+
section DPBounds
... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_fa5a88b92d24_2 | 2b5d597e5c1cce31 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/Histogram/Properties.lean | Properties | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "privNoisedBinCount_DP",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold privNoisedBinCount\n apply dpn.noise_prop HN_bin\n apply exactBinCount_sensitivity",
"n_chars": 95,
... | [
{
"name": "exactBinCount_sensitivity",
"text": "theorem exactBinCount_sensitivity (b : Fin numBins) : sensitivity (exactBinCount numBins B b) 1 := by\n rw [sensitivity]\n intros _ _ H\n cases H\n all_goals simp_all [exactBinCount, exactBinCount, List.filter_cons]\n all_goals aesop\n\n",
"fan_in": 1... | [
{
"name": "privNoisedHistogram_DP",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 11,
"n_chars": 380,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Queries.Histogram.Code
import SampCert.DifferentialPrivacy.Sensitivity
import SampCert.DifferentialPriv... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Queries.Histogram.Code
import SampCert.DifferentialPrivacy.Sensitivity
import SampCert.DifferentialPriv... | @@ -26,6 +26,13 @@
/-
exactBinCount is 1-sensitive
-/
+theorem exactBinCount_sensitivity (b : Fin numBins) : sensitivity (exactBinCount numBins B b) 1 := by
+ rw [sensitivity]
+ intros _ _ H
+ cases H
+ all_goals simp_all [exactBinCount, exactBinCount, List.filter_cons]
+ all_goals aesop
+
section DPBounds
... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_fa5a88b92d24_3 | 344e14c01113514b | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/Histogram/Properties.lean | Properties | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "privNoisedBinCount_DP",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold privNoisedBinCount\n apply dpn.noise_prop HN_bin\n apply exactBinCount_sensitivity",
"n_chars": 95,
... | [
{
"name": "exactBinCount_sensitivity",
"text": "theorem exactBinCount_sensitivity (b : Fin numBins) : sensitivity (exactBinCount numBins B b) 1 := by\n rw [sensitivity]\n intros _ _ H\n cases H\n all_goals simp_all [exactBinCount, exactBinCount, List.filter_cons]\n all_goals aesop\n\n",
"fan_in": 1... | [
{
"name": "privMaxBinAboveThreshold_DP",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 12,
"n_chars": 345,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
... | 4 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Queries.Histogram.Code
import SampCert.DifferentialPrivacy.Sensitivity
import SampCert.DifferentialPriv... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Queries.Histogram.Code
import SampCert.DifferentialPrivacy.Sensitivity
import SampCert.DifferentialPriv... | @@ -26,6 +26,13 @@
/-
exactBinCount is 1-sensitive
-/
+theorem exactBinCount_sensitivity (b : Fin numBins) : sensitivity (exactBinCount numBins B b) 1 := by
+ rw [sensitivity]
+ intros _ _ H
+ cases H
+ all_goals simp_all [exactBinCount, exactBinCount, List.filter_cons]
+ all_goals aesop
+
section DPBounds
... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_906f66494931_0 | 8de10fc3890b96e8 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/LaplaceGen/Properties.lean | Properties | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "DiscreteLaplaceGenSample_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Summable.hasSum_iff ENNReal.summable]\n conv =>\n enter [1, 1, b]\n rw [DiscreteLaplaceGenSample_p... | [
{
"name": "DiscreteLaplaceGenSample_periodic",
"text": "theorem DiscreteLaplaceGenSample_periodic (num : PNat) (den : PNat) (μ x : ℤ) :\n (DiscreteLaplaceGenSample num den μ) x =\n (DiscreteLaplaceSample num den) (x - μ) := by\n simp [DiscreteLaplaceGenSample]\n rw [tsum_eq_single (x - μ) (by aesop)]\... | [
{
"name": "DiscreteLaplaceGenSample_sum",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 22,
"n_chars": 542,
"n_subproofs": 0,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 4,
"n_structural": 7,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Samplers.LaplaceGen.Code
import SampCert.Samplers.Laplace.Basic
import SampCert.Util.Shift
noncomputable section
open Cl... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Samplers.LaplaceGen.Code
import SampCert.Samplers.Laplace.Basic
import SampCert.Util.Shift
noncomputable section
open Cl... | @@ -22,10 +22,33 @@
rw [tsum_eq_single (x - μ) (by aesop)]
simp
+theorem DiscreteLaplaceGenSample_periodic (num : PNat) (den : PNat) (μ x : ℤ) :
+ (DiscreteLaplaceGenSample num den μ) x =
+ (DiscreteLaplaceSample num den) (x - μ) := by
+ simp [DiscreteLaplaceGenSample]
+ rw [tsum_eq_single (x - μ) (by aes... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_0 | 35a9e64f5fda3ed6 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 4 | [
{
"theorem_name": "RenyiDivergence_def_exp",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Unfold the definition and group the `(α-1)` factors together so they cancel.\n rw [RenyiDivergence_def, ← mul_a... | [
{
"name": "EReal_coe_sub_one",
"text": "/--\nRearrange the definition of ``RenyiDivergence_def`` to obtain an equation for the inner series.\n-/\nlemma EReal_coe_sub_one (α : ℝ) :\n (α.toEReal - OfNat.ofNat 1) = ((α - 1 : ℝ) : EReal) := by\n rw [← EReal.coe_one, ← EReal.coe_sub]\n\n",
"fan_in": 4,
... | [
{
"name": "RenyiDivergence_def_exp",
"fan_in": 4,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 601,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 0,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -32,12 +32,21 @@
noncomputable def RenyiDivergence_def (p q : PMF T) (α : ℝ) : EReal :=
(α - 1)⁻¹ * (elog (∑' x : T, (p x)^α * (q x)^(1 - α)))
+/--
+Rearrange the definition of ``RenyiDivergence_def`` to obtain an equation for the inner series.
+-/
+lemma EReal_coe_sub_one (α : ℝ) :
+ (α.toEReal - OfNat.o... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_1 | 5abbd29772ae1693 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 4 | [
{
"theorem_name": "RenyiDivergence_def_exp",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Unfold the definition and group the `(α-1)` factors together so they cancel.\n rw [RenyiDivergence_def, ← mul_a... | [
{
"name": "EReal_coe_sub_one",
"text": "/--\nRearrange the definition of ``RenyiDivergence_def`` to obtain an equation for the inner series.\n-/\nlemma EReal_coe_sub_one (α : ℝ) :\n (α.toEReal - OfNat.ofNat 1) = ((α - 1 : ℝ) : EReal) := by\n rw [← EReal.coe_one, ← EReal.coe_sub]\n\n",
"fan_in": 4,
... | [
{
"name": "EReal_sub_one_pos_of_one_lt",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 171,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -32,8 +32,16 @@
noncomputable def RenyiDivergence_def (p q : PMF T) (α : ℝ) : EReal :=
(α - 1)⁻¹ * (elog (∑' x : T, (p x)^α * (q x)^(1 - α)))
+/--
+Rearrange the definition of ``RenyiDivergence_def`` to obtain an equation for the inner series.
+-/
+lemma EReal_coe_sub_one (α : ℝ) :
+ (α.toEReal - OfNat.of... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_2 | 865fd0eba80114f1 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 4 | [
{
"theorem_name": "RenyiDivergence_def_exp",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Unfold the definition and group the `(α-1)` factors together so they cancel.\n rw [RenyiDivergence_def, ← mul_a... | [
{
"name": "EReal_coe_sub_one",
"text": "/--\nRearrange the definition of ``RenyiDivergence_def`` to obtain an equation for the inner series.\n-/\nlemma EReal_coe_sub_one (α : ℝ) :\n (α.toEReal - OfNat.ofNat 1) = ((α - 1 : ℝ) : EReal) := by\n rw [← EReal.coe_one, ← EReal.coe_sub]\n\n",
"fan_in": 4,
... | [
{
"name": "EReal_sub_one_lt_top",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 137,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -32,8 +32,16 @@
noncomputable def RenyiDivergence_def (p q : PMF T) (α : ℝ) : EReal :=
(α - 1)⁻¹ * (elog (∑' x : T, (p x)^α * (q x)^(1 - α)))
+/--
+Rearrange the definition of ``RenyiDivergence_def`` to obtain an equation for the inner series.
+-/
+lemma EReal_coe_sub_one (α : ℝ) :
+ (α.toEReal - OfNat.of... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_3 | 59b3e2b27a810ef0 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "RenyiDivergenceExpectation",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine tsum_congr (fun x => ?_)\n exact RenyiDivergenceExpectation_pointwise (p x) (q x) h (H x)",
"n_chars... | [
{
"name": "RenyiDivergenceExpectation_pointwise",
"text": "lemma RenyiDivergenceExpectation_pointwise (a b : ENNReal) {α : ℝ} (h : 1 < α)\n (Hac : b = 0 → a = 0) : a ^ α * b ^ (1 - α) = (a / b) ^ α * b := by\n rcases eq_or_ne b 0 with hb0 | hb0\n · -- b = 0: a = 0 by AbsCts, so both sides vanish.\n ... | [
{
"name": "RenyiDivergenceExpectation",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 375,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -32,11 +32,48 @@
noncomputable def RenyiDivergence_def (p q : PMF T) (α : ℝ) : EReal :=
(α - 1)⁻¹ * (elog (∑' x : T, (p x)^α * (q x)^(1 - α)))
+lemma RenyiDivergenceExpectation_pointwise (a b : ENNReal) {α : ℝ} (h : 1 < α)
+ (Hac : b = 0 → a = 0) : a ^ α * b ^ (1 - α) = (a / b) ^ α * b := by
+ rcases eq_... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_4 | b36fff2adb6bc8f5 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "RenyiDivergenceExpectation'_pointwise",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases eq_or_ne b 0 with hb0 | hb0\n · -- b = 0: both sides equal `⊤ * a`.\n subst hb0\n rw [... | [
{
"name": "ENNReal_rpow_sub_one_mul",
"text": "lemma ENNReal_rpow_sub_one_mul (a : ENNReal) {α : ℝ}\n (ha_ne_zero : a ≠ 0) (ha_ne_top : a ≠ ⊤) :\n a ^ (α - 1) * a = a ^ α := by\n conv_rhs => rw [show α = (α - 1) + 1 from by ring]\n rw [ENNReal.rpow_add _ _ ha_ne_zero ha_ne_top, ENNReal.rpow_one]\n\n... | [
{
"name": "RenyiDivergenceExpectation'_pointwise",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 26,
"n_chars": 1184,
"n_subproofs": 0,
"n_tactics": 23,
"cyclomatic": 3,
"n_automation": 8,
"n_rewrites": 14,
"n_structural": 4,
"automation_only... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -32,9 +32,36 @@
noncomputable def RenyiDivergence_def (p q : PMF T) (α : ℝ) : EReal :=
(α - 1)⁻¹ * (elog (∑' x : T, (p x)^α * (q x)^(1 - α)))
+lemma ENNReal_rpow_sub_one_mul (a : ENNReal) {α : ℝ}
+ (ha_ne_zero : a ≠ 0) (ha_ne_top : a ≠ ⊤) :
+ a ^ (α - 1) * a = a ^ α := by
+ conv_rhs => rw [show α = (α... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_5 | c584256ec2d5b997 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "RenyiDivergenceExpectation'_pointwise",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases eq_or_ne b 0 with hb0 | hb0\n · -- b = 0: both sides equal `⊤ * a`.\n subst hb0\n rw [... | [
{
"name": "ENNReal_rpow_sub_one_mul",
"text": "lemma ENNReal_rpow_sub_one_mul (a : ENNReal) {α : ℝ}\n (ha_ne_zero : a ≠ 0) (ha_ne_top : a ≠ ⊤) :\n a ^ (α - 1) * a = a ^ α := by\n conv_rhs => rw [show α = (α - 1) + 1 from by ring]\n rw [ENNReal.rpow_add _ _ ha_ne_zero ha_ne_top, ENNReal.rpow_one]\n\n... | [
{
"name": "RenyiDivergenceExpectation'",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 22,
"n_chars": 931,
"n_subproofs": 2,
"n_tactics": 16,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 6,
"n_structural": 6,
"automation_only": false,
... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -32,9 +32,36 @@
noncomputable def RenyiDivergence_def (p q : PMF T) (α : ℝ) : EReal :=
(α - 1)⁻¹ * (elog (∑' x : T, (p x)^α * (q x)^(1 - α)))
+lemma ENNReal_rpow_sub_one_mul (a : ENNReal) {α : ℝ}
+ (ha_ne_zero : a ≠ 0) (ha_ne_top : a ≠ ⊤) :
+ a ^ (α - 1) * a = a ^ α := by
+ conv_rhs => rw [show α = (α... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_6 | e96220138281c7a1 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "Integrable_rpow_of_one_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hα0 : ENNReal.ofReal α ≠ 0 := by simp; linarith\n have hαt : ENNReal.ofReal α ≠ ⊤ := by simp\n have Z := I... | [
{
"name": "Integrable_rpow",
"text": "lemma Integrable_rpow (f : T → ℝ) (nn : ∀ x : T, 0 ≤ f x) (μ : Measure T) (α : ENNReal)\n (mem : MemLp f α μ) (h1 : α ≠ 0) (h2 : α ≠ ⊤) :\n MeasureTheory.Integrable (fun x : T => (f x) ^ α.toReal) μ := by\n have HRP := @MeasureTheory.MemLp.integrable_norm_rpow T ... | [
{
"name": "Integrable_rpow_of_one_lt",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 472,
"n_subproofs": 3,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -46,10 +46,22 @@
variable [disc : DiscreteMeasurableSpace U]
variable [Inhabited U]
+lemma Integrable_rpow (f : T → ℝ) (nn : ∀ x : T, 0 ≤ f x) (μ : Measure T) (α : ENNReal)
+ (mem : MemLp f α μ) (h1 : α ≠ 0) (h2 : α ≠ ⊤) :
+ MeasureTheory.Integrable (fun x : T => (f x) ^ α.toReal) μ := by
+ have HRP := @M... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_7 | 867075e500c4eee6 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 2 | [
{
"theorem_name": "Renyi_Jensen_real",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp_rw [show ∀ x : T, f x * (q x).toReal = (q x).toReal • f x from\n fun x => by rw [smul_eq_mul, mul_comm]]\n simp... | [
{
"name": "Integrable_rpow_of_one_lt",
"text": "lemma Integrable_rpow_of_one_lt {f : T → ℝ} {α : ℝ} (h : 1 < α)\n (h2 : ∀ x : T, 0 ≤ f x) {μ : Measure T}\n (mem : MemLp f (ENNReal.ofReal α) μ) :\n MeasureTheory.Integrable (fun x : T => f x ^ α) μ := by\n have hα0 : ENNReal.ofReal α ≠ 0 := by simp;... | [
{
"name": "Renyi_Jensen_real",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 29,
"n_chars": 1448,
"n_subproofs": 4,
"n_tactics": 20,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 7,
"n_structural": 6,
"automation_only": false,
"max_ne... | 4 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -62,6 +62,15 @@
· exact Or.inr (lt_trans zero_lt_one h)
· exact Or.inl hxpos.ne'
+lemma Integrable_rpow_of_one_lt {f : T → ℝ} {α : ℝ} (h : 1 < α)
+ (h2 : ∀ x : T, 0 ≤ f x) {μ : Measure T}
+ (mem : MemLp f (ENNReal.ofReal α) μ) :
+ MeasureTheory.Integrable (fun x : T => f x ^ α) μ := by
+ have hα0 :... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_8 | 2076eed25f7e6a97 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 2 | [
{
"theorem_name": "Renyi_Jensen_real",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp_rw [show ∀ x : T, f x * (q x).toReal = (q x).toReal • f x from\n fun x => by rw [smul_eq_mul, mul_comm]]\n simp... | [
{
"name": "Integrable_rpow_of_one_lt",
"text": "lemma Integrable_rpow_of_one_lt {f : T → ℝ} {α : ℝ} (h : 1 < α)\n (h2 : ∀ x : T, 0 ≤ f x) {μ : Measure T}\n (mem : MemLp f (ENNReal.ofReal α) μ) :\n MeasureTheory.Integrable (fun x : T => f x ^ α) μ := by\n have hα0 : ENNReal.ofReal α ≠ 0 := by simp;... | [
{
"name": "Renyi_Jensen_strict_real",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 53,
"n_chars": 2961,
"n_subproofs": 8,
"n_tactics": 47,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 12,
"n_structural": 9,
"automation_only": false,
... | 4 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -62,6 +62,15 @@
· exact Or.inr (lt_trans zero_lt_one h)
· exact Or.inl hxpos.ne'
+lemma Integrable_rpow_of_one_lt {f : T → ℝ} {α : ℝ} (h : 1 < α)
+ (h2 : ∀ x : T, 0 ≤ f x) {μ : Measure T}
+ (mem : MemLp f (ENNReal.ofReal α) μ) :
+ MeasureTheory.Integrable (fun x : T => f x ^ α) μ := by
+ have hα0 :... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_9 | d75734c8a2b892a9 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "PMF_div_mul_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [division_def, mul_mul_inv_eq_mul_cancel (H z) (PMF_q_ne_top_pq p q z)]",
"n_chars": 80,
"n_subproofs": 0,
"n... | [
{
"name": "PMF_q_ne_top_pq",
"text": "lemma PMF_q_ne_top_pq (p q : PMF T) (z : T) : ¬(p z ≠ 0 ∧ q z = ⊤) :=\n fun ⟨_, hqt⟩ => PMF.apply_ne_top q z hqt\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 125,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_re... | [
{
"name": "PMF_div_mul_eq",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 168,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting"... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -53,8 +53,12 @@
-/
noncomputable def Renyi_Jensen_f (p q : PMF T) : T → ℝ := (fun z => (p z / q z).toReal)
-lemma PMF_div_mul_eq (p q : PMF T) (H : AbsCts p q) (z : T) : p z / q z * q z = p z := sorry
+lemma PMF_q_ne_top_pq (p q : PMF T) (z : T) : ¬(p z ≠ 0 ∧ q z = ⊤) :=
+ fun ⟨_, hqt⟩ => PMF.apply_ne_top q z h... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_10 | 003a9025ff724a19 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 3 | [
{
"theorem_name": "Renyi_Jensen_rw",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold Renyi_Jensen_f\n rw [ENNReal.toReal_rpow, ← ENNReal.toReal_mul, ENNReal.ofReal_toReal]\n refine mul_ne_top (rpow_n... | [
{
"name": "Renyi_Jensen_div_ne_top",
"text": "/--\nSummand from the Renyi divergence equals a real-valued summand, except in a special case.\n-/\nlemma Renyi_Jensen_div_ne_top (p q : PMF T) (H : AbsCts p q)\n (Hspecial : ∀ x : T, ¬(p x = ⊤ ∧ q x ≠ 0 ∧ q x ≠ ⊤)) (a : T) : p a / q a ≠ ⊤ := by\n intro HK\n... | [
{
"name": "Renyi_Jensen_rw",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 482,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -53,9 +53,27 @@
-/
noncomputable def Renyi_Jensen_f (p q : PMF T) : T → ℝ := (fun z => (p z / q z).toReal)
+/--
+Summand from the Renyi divergence equals a real-valued summand, except in a special case.
+-/
+lemma Renyi_Jensen_div_ne_top (p q : PMF T) (H : AbsCts p q)
+ (Hspecial : ∀ x : T, ¬(p x = ⊤ ∧ q x ≠ ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_11 | 46081fece351e238 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 3 | [
{
"theorem_name": "Renyi_Jensen_rw",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold Renyi_Jensen_f\n rw [ENNReal.toReal_rpow, ← ENNReal.toReal_mul, ENNReal.ofReal_toReal]\n refine mul_ne_top (rpow_n... | [
{
"name": "Renyi_Jensen_div_ne_top",
"text": "/--\nSummand from the Renyi divergence equals a real-valued summand, except in a special case.\n-/\nlemma Renyi_Jensen_div_ne_top (p q : PMF T) (H : AbsCts p q)\n (Hspecial : ∀ x : T, ¬(p x = ⊤ ∧ q x ≠ 0 ∧ q x ≠ ⊤)) (a : T) : p a / q a ≠ ⊤ := by\n intro HK\n... | [
{
"name": "Renyi_Jensen_f_MemLp",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 35,
"n_chars": 1850,
"n_subproofs": 5,
"n_tactics": 30,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 10,
"n_structural": 9,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -53,11 +53,53 @@
-/
noncomputable def Renyi_Jensen_f (p q : PMF T) : T → ℝ := (fun z => (p z / q z).toReal)
+/--
+Summand from the Renyi divergence equals a real-valued summand, except in a special case.
+-/
+lemma Renyi_Jensen_div_ne_top (p q : PMF T) (H : AbsCts p q)
+ (Hspecial : ∀ x : T, ¬(p x = ⊤ ∧ q x ≠... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_12 | da5b6d05f6fd272a | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 2 | [
{
"theorem_name": "Renyi_Jensen_real",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp_rw [show ∀ x : T, f x * (q x).toReal = (q x).toReal • f x from\n fun x => by rw [smul_eq_mul, mul_comm]]\n simp... | [
{
"name": "Integrable_of_MemLp_one_lt",
"text": "lemma Integrable_of_MemLp_one_lt {f : T → ℝ} {α : ℝ} (h : 1 < α)\n {μ : Measure T} [IsFiniteMeasure μ]\n (mem : MemLp f (ENNReal.ofReal α) μ) : MeasureTheory.Integrable f μ := by\n apply MeasureTheory.MemLp.integrable _ mem\n rw [one_le_ofReal]; exact... | [
{
"name": "Renyi_Jensen_ENNReal_reduct",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 9,
"n_lines": 62,
"n_chars": 3473,
"n_subproofs": 12,
"n_tactics": 53,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 11,
"n_structural": 15,
"automation_only": false... | 9 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -77,6 +77,12 @@
have Z := Integrable_rpow f h2 μ (ENNReal.ofReal α) mem hα0 hαt
rwa [toReal_ofReal (le_of_lt (lt_trans zero_lt_one h))] at Z
+lemma Integrable_of_MemLp_one_lt {f : T → ℝ} {α : ℝ} (h : 1 < α)
+ {μ : Measure T} [IsFiniteMeasure μ]
+ (mem : MemLp f (ENNReal.ofReal α) μ) : MeasureTheory.Int... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_13 | 6228461b7e2be7e8 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "Renyi_Jensen_ENNReal_converse_reduct",
"depth": 1,
"n_commands": 0,
"n_lines": 83,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n haveI : DiscreteMeasurableSpace T := MeasurableSingletonClass.toDiscreteMeasurableSpace\n by_cases H... | [
{
"name": "Renyi_Jensen_strict_real",
"text": "/--\nStrict version of Jensen's inequality applied to the function ``(⬝)^α``.\n-/\ntheorem Renyi_Jensen_strict_real [t2 : MeasurableSingletonClass T] [tcount : Countable T] (f : T → ℝ) (q : PMF T) (α : ℝ) (h : 1 < α) (h2 : ∀ x : T, 0 ≤ f x) (mem : MemLp f (ENNR... | [
{
"name": "Renyi_Jensen_ENNReal_converse_reduct",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 11,
"n_lines": 91,
"n_chars": 4948,
"n_subproofs": 17,
"n_tactics": 76,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 15,
"n_structural": 19,
"automation_on... | 11 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -83,6 +83,58 @@
apply MeasureTheory.MemLp.integrable _ mem
rw [one_le_ofReal]; exact le_of_lt h
+/--
+Strict version of Jensen's inequality applied to the function ``(⬝)^α``.
+-/
+theorem Renyi_Jensen_strict_real [t2 : MeasurableSingletonClass T] [tcount : Countable T] (f : T → ℝ) (q : PMF T) (α : ℝ) (h : 1 ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_14 | 8e24bddebb75cc0a | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 2 | [
{
"theorem_name": "Renyi_Jensen_real",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp_rw [show ∀ x : T, f x * (q x).toReal = (q x).toReal • f x from\n fun x => by rw [smul_eq_mul, mul_comm]]\n simp... | [
{
"name": "Integrable_of_MemLp_one_lt",
"text": "lemma Integrable_of_MemLp_one_lt {f : T → ℝ} {α : ℝ} (h : 1 < α)\n {μ : Measure T} [IsFiniteMeasure μ]\n (mem : MemLp f (ENNReal.ofReal α) μ) : MeasureTheory.Integrable f μ := by\n apply MeasureTheory.MemLp.integrable _ mem\n rw [one_le_ofReal]; exact... | [
{
"name": "Renyi_Jensen_ENNReal",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 14,
"n_lines": 14,
"n_chars": 612,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 3,
"automation_only": false,
"max_... | 13 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -82,6 +82,12 @@
have Z := Integrable_rpow f h2 μ (ENNReal.ofReal α) mem hα0 hαt
rwa [toReal_ofReal (le_of_lt (lt_trans zero_lt_one h))] at Z
+lemma Integrable_of_MemLp_one_lt {f : T → ℝ} {α : ℝ} (h : 1 < α)
+ {μ : Measure T} [IsFiniteMeasure μ]
+ (mem : MemLp f (ENNReal.ofReal α) μ) : MeasureTheory.Int... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_15 | cadc0b88333e9994 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 3 | [
{
"theorem_name": "Renyi_Jensen_rw",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold Renyi_Jensen_f\n rw [ENNReal.toReal_rpow, ← ENNReal.toReal_mul, ENNReal.ofReal_toReal]\n refine mul_ne_top (rpow_n... | [
{
"name": "Renyi_Jensen_div_ne_top",
"text": "/--\nSummand from the Renyi divergence equals a real-valued summand, except in a special case.\n-/\nlemma Renyi_Jensen_div_ne_top (p q : PMF T) (H : AbsCts p q)\n (Hspecial : ∀ x : T, ¬(p x = ⊤ ∧ q x ≠ 0 ∧ q x ≠ ⊤)) (a : T) : p a / q a ≠ ⊤ := by\n intro HK\n... | [
{
"name": "Renyi_Jensen_ENNReal_converse",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 16,
"n_lines": 26,
"n_chars": 1127,
"n_subproofs": 3,
"n_tactics": 19,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 9,
"automation_only": false... | 15 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -147,6 +147,20 @@
-/
noncomputable def Renyi_Jensen_f (p q : PMF T) : T → ℝ := (fun z => (p z / q z).toReal)
+/--
+Summand from the Renyi divergence equals a real-valued summand, except in a special case.
+-/
+lemma Renyi_Jensen_div_ne_top (p q : PMF T) (H : AbsCts p q)
+ (Hspecial : ∀ x : T, ¬(p x = ⊤ ∧ q x ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_16 | 9d3adfe70ed8bb79 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 3 | [
{
"theorem_name": "RenyiDivergence_def_nonneg",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have H1 : eexp (((α - 1)) * 0) ≤ eexp ((α - 1) * RenyiDivergence_def p q α) := by\n rw [RenyiDivergence_def... | [
{
"name": "RenyiDivergenceExpectation",
"text": "/--\nRenyi Divergence series written as a conditional expectation, conditioned on q.\n-/\ntheorem RenyiDivergenceExpectation (p q : T → ENNReal) {α : ℝ} (h : 1 < α) (H : AbsCts p q) :\n (∑' x : T, (p x)^α * (q x)^(1 - α)) = ∑' x : T, (p x / q x)^α * (q x) ... | [
{
"name": "RenyiDivergence_def_nonneg",
"fan_in": 2,
"n_deps_direct": 6,
"n_deps_transitive": 21,
"n_lines": 27,
"n_chars": 1129,
"n_subproofs": 3,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 6,
"automation_only": false,
... | 20 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -103,6 +103,14 @@
rw [ENNReal.rpow_sub _ _ hb0 hbt, ← ENNReal.mul_comm_div,
← ENNReal.div_rpow_of_nonneg _ _ (by linarith : (0 : ℝ) ≤ α), ENNReal.rpow_one]
+/--
+Renyi Divergence series written as a conditional expectation, conditioned on q.
+-/
+theorem RenyiDivergenceExpectation (p q : T → ENNReal) {α ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_17 | 5688ecf8fe8b1578 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 4 | [
{
"theorem_name": "RenyiDivergence_def_nonneg",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have H1 : eexp (((α - 1)) * 0) ≤ eexp ((α - 1) * RenyiDivergence_def p q α) := by\n rw [RenyiDivergence_def... | [
{
"name": "RenyiDivergence_def_exp",
"text": "lemma RenyiDivergence_def_exp (p q : PMF T) {α : ℝ} (h : 1 < α) :\n eexp ((α - 1) * RenyiDivergence_def p q α) = (∑' x : T, (p x)^α * (q x)^(1 - α)) := by\n -- Unfold the definition and group the `(α-1)` factors together so they cancel.\n rw [RenyiDivergenc... | [
{
"name": "RenyiDivergence_refl_zero",
"fan_in": 2,
"n_deps_direct": 5,
"n_deps_transitive": 7,
"n_lines": 22,
"n_chars": 816,
"n_subproofs": 3,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 6,
"n_structural": 4,
"automation_only": false,
... | 7 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -44,6 +44,16 @@
(α.toEReal - OfNat.ofNat 1) = ((α - 1 : ℝ) : EReal) := by
rw [← EReal.coe_one, ← EReal.coe_sub]
+lemma RenyiDivergence_def_exp (p q : PMF T) {α : ℝ} (h : 1 < α) :
+ eexp ((α - 1) * RenyiDivergence_def p q α) = (∑' x : T, (p x)^α * (q x)^(1 - α)) := by
+ -- Unfold the definition and grou... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_18 | a5172b4a1628ac93 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 2 | [
{
"theorem_name": "Renyi_Jensen_real",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp_rw [show ∀ x : T, f x * (q x).toReal = (q x).toReal • f x from\n fun x => by rw [smul_eq_mul, mul_comm]]\n simp... | [
{
"name": "continuousOn_rpow_Ici_of_one_lt",
"text": "lemma continuousOn_rpow_Ici_of_one_lt {α : ℝ} (h : 1 < α) :\n ContinuousOn (fun x : ℝ => x ^ α) (Set.Ici 0) := by\n apply ContinuousOn.rpow continuousOn_id continuousOn_const\n intro x hx\n rcases (Set.mem_Ici.mp hx).lt_or_eq.symm.imp Eq.symm id wi... | [
{
"name": "RenyiDivergence_def_eq_0_iff",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 24,
"n_lines": 26,
"n_chars": 800,
"n_subproofs": 1,
"n_tactics": 19,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 5,
"n_structural": 8,
"automation_only": false,
... | 23 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -133,6 +133,14 @@
funext x; rw [Real.norm_of_nonneg (nn x)]
rwa [Hcongr] at HRP
+lemma continuousOn_rpow_Ici_of_one_lt {α : ℝ} (h : 1 < α) :
+ ContinuousOn (fun x : ℝ => x ^ α) (Set.Ici 0) := by
+ apply ContinuousOn.rpow continuousOn_id continuousOn_const
+ intro x hx
+ rcases (Set.mem_Ici.mp hx).lt_... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_19 | 82a3c3f2da23fc37 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "Integrable_rpow_of_one_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hα0 : ENNReal.ofReal α ≠ 0 := by simp; linarith\n have hαt : ENNReal.ofReal α ≠ ⊤ := by simp\n have Z := I... | [
{
"name": "Integrable_rpow",
"text": "lemma Integrable_rpow (f : T → ℝ) (nn : ∀ x : T, 0 ≤ f x) (μ : Measure T) (α : ENNReal)\n (mem : MemLp f α μ) (h1 : α ≠ 0) (h2 : α ≠ ⊤) :\n MeasureTheory.Integrable (fun x : T => (f x) ^ α.toReal) μ := by\n have HRP := @MeasureTheory.MemLp.integrable_norm_rpow T ... | [
{
"name": "RenyiDivergence_def_log_sum_nonneg",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 22,
"n_lines": 13,
"n_chars": 488,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": fa... | 21 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -125,6 +125,14 @@
variable [disc : DiscreteMeasurableSpace U]
variable [Inhabited U]
+lemma Integrable_rpow (f : T → ℝ) (nn : ∀ x : T, 0 ≤ f x) (μ : Measure T) (α : ENNReal)
+ (mem : MemLp f α μ) (h1 : α ≠ 0) (h2 : α ≠ ⊤) :
+ MeasureTheory.Integrable (fun x : T => (f x) ^ α.toReal) μ := by
+ have HRP := @... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_20 | 531a85f286a33cd5 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 2 | [
{
"theorem_name": "Renyi_Jensen_real",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp_rw [show ∀ x : T, f x * (q x).toReal = (q x).toReal • f x from\n fun x => by rw [smul_eq_mul, mul_comm]]\n simp... | [
{
"name": "Integrable_rpow_of_one_lt",
"text": "lemma Integrable_rpow_of_one_lt {f : T → ℝ} {α : ℝ} (h : 1 < α)\n (h2 : ∀ x : T, 0 ≤ f x) {μ : Measure T}\n (mem : MemLp f (ENNReal.ofReal α) μ) :\n MeasureTheory.Integrable (fun x : T => f x ^ α) μ := by\n have hα0 : ENNReal.ofReal α ≠ 0 := by simp;... | [
{
"name": "RenyiDivergence_aux_zero",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 29,
"n_lines": 22,
"n_chars": 704,
"n_subproofs": 1,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 6,
"automation_only": false,
... | 28 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -141,6 +141,15 @@
· exact Or.inr (lt_trans zero_lt_one h)
· exact Or.inl hxpos.ne'
+lemma Integrable_rpow_of_one_lt {f : T → ℝ} {α : ℝ} (h : 1 < α)
+ (h2 : ∀ x : T, 0 ≤ f x) {μ : Measure T}
+ (mem : MemLp f (ENNReal.ofReal α) μ) :
+ MeasureTheory.Integrable (fun x : T => f x ^ α) μ := by
+ have hα0... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_251989bdb02f_21 | 7570d845720a1d2d | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/RenyiDivergence.lean | RenyiDivergence | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 4 | [
{
"theorem_name": "RenyiDivergence_def_nonneg",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have H1 : eexp (((α - 1)) * 0) ≤ eexp ((α - 1) * RenyiDivergence_def p q α) := by\n rw [RenyiDivergence_def... | [
{
"name": "RenyiDivergence_def_exp",
"text": "lemma RenyiDivergence_def_exp (p q : PMF T) {α : ℝ} (h : 1 < α) :\n eexp ((α - 1) * RenyiDivergence_def p q α) = (∑' x : T, (p x)^α * (q x)^(1 - α)) := by\n -- Unfold the definition and group the `(α-1)` factors together so they cancel.\n rw [RenyiDivergenc... | [
{
"name": "RenyiDivergence_le_MaxDivergence",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 46,
"n_chars": 1381,
"n_subproofs": 2,
"n_tactics": 35,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 13,
"n_structural": 13,
"automation_only": f... | 6 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Topology.Algebra.InfiniteSum.Ring
import Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable
import Mathlib.Analysis.S... | @@ -39,6 +39,16 @@
(α.toEReal - OfNat.ofNat 1) = ((α - 1 : ℝ) : EReal) := by
rw [← EReal.coe_one, ← EReal.coe_sub]
+lemma RenyiDivergence_def_exp (p q : PMF T) {α : ℝ} (h : 1 < α) :
+ eexp ((α - 1) * RenyiDivergence_def p q α) = (∑' x : T, (p x)^α * (q x)^(1 - α)) := by
+ -- Unfold the definition and grou... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b033140d58d1_0 | cf9da3e32936976c | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/Postprocessing.lean | Postprocessing | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "δpmf_conv'",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext x\n rw [δpmf_conv]",
"n_chars": 29,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": ... | [
{
"name": "δpmf_conv",
"text": "theorem δpmf_conv (nq : SLang U) (a : V) (x : {n | a = f n}) (h1 : ∑' (i : ↑{n | a = f n}), nq ↑i ≠ 0) (h2 : ∑' (i : ↑{n | a = f n}), nq ↑i ≠ ⊤) :\n nq x * (∑' (x : {n | a = f n}), nq x)⁻¹ = (δpmf nq f a h1 h2) x := by\n simp [δpmf]\n conv =>\n right\n left\n left... | [
{
"name": "δpmf_conv'",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 291,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# Postprocessing
This file proves... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# Postprocessing
This file proves... | @@ -43,8 +43,19 @@
def δpmf (nq : SLang U) (f : U → V) (a : V) (h1 : ∑' (i : ↑{n | a = f n}), nq ↑i ≠ 0) (h2 : ∑' (i : ↑{n | a = f n}), nq ↑i ≠ ⊤) : PMF {n : U | a = f n} :=
⟨ δ nq f a , δ_normalizes nq f a h1 h2 ⟩
+theorem δpmf_conv (nq : SLang U) (a : V) (x : {n | a = f n}) (h1 : ∑' (i : ↑{n | a = f n}), nq ↑i ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b033140d58d1_1 | c1a28b943159f554 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/Postprocessing.lean | Postprocessing | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "ENNReal.tsum_pos_int",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply ENNReal.tsum_pos h1 h2 42",
"n_chars": 37,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
... | [
{
"name": "ENNReal.tsum_pos",
"text": "theorem ENNReal.tsum_pos {f : T → ENNReal} (h1 : ∑' x : T, f x ≠ ⊤) (h2 : ∀ x : T, f x ≠ 0) (i : T) :\n 0 < ∑' x : T, f x := by\n apply (toNNReal_lt_toNNReal ENNReal.zero_ne_top h1).mp\n simp only [ENNReal.toNNReal_zero]\n rw [ENNReal.tsum_toNNReal_eq (ENNReal.ne_t... | [
{
"name": "ENNReal.tsum_pos_int",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# Postprocessing
This file proves... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# Postprocessing
This file proves... | @@ -43,8 +43,26 @@
def δpmf (nq : SLang U) (f : U → V) (a : V) (h1 : ∑' (i : ↑{n | a = f n}), nq ↑i ≠ 0) (h2 : ∑' (i : ↑{n | a = f n}), nq ↑i ≠ ⊤) : PMF {n : U | a = f n} :=
⟨ δ nq f a , δ_normalizes nq f a h1 h2 ⟩
+theorem ENNReal.tsum_pos {f : T → ENNReal} (h1 : ∑' x : T, f x ≠ ⊤) (h2 : ∀ x : T, f x ≠ 0) (i : T... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b033140d58d1_2 | 1ada9d70a4e8f523 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/Postprocessing.lean | Postprocessing | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "privPostPocess_DP_pre_reduct",
"depth": 1,
"n_commands": 0,
"n_lines": 276,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n\n -- By absolute continuity, nq1 is nonzero\n have Hnql1 : (∀ (u : U), nq l₂ u ≠ 0) := by\n rw [AbsCts] ... | [
{
"name": "convergent_subset",
"text": "theorem convergent_subset {p : T → ENNReal} (f : T → V) (conv : ∑' (x : T), p x ≠ ⊤) :\n ∑' (x : { y : T| x = f y }), p x ≠ ⊤ := by\n rw [← condition_to_subset]\n have A : (∑' (y : T), if x = f y then p y else 0) ≤ ∑' (x : T), p x := by\n apply ENNReal.tsum_le_... | [
{
"name": "privPostPocess_DP_pre_reduct",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 290,
"n_chars": 8287,
"n_subproofs": 21,
"n_tactics": 238,
"cyclomatic": 15,
"n_automation": 29,
"n_rewrites": 64,
"n_structural": 73,
"automation_only": ... | 3 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# Postprocessing
This file proves... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# Postprocessing
This file proves... | @@ -48,6 +48,20 @@
rw [← nonempty_subtype]
exact Set.nonempty_iff_ne_empty'.mpr h
+theorem convergent_subset {p : T → ENNReal} (f : T → V) (conv : ∑' (x : T), p x ≠ ⊤) :
+ ∑' (x : { y : T| x = f y }), p x ≠ ⊤ := by
+ rw [← condition_to_subset]
+ have A : (∑' (y : T), if x = f y then p y else 0) ≤ ∑' (x : T)... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b033140d58d1_3 | 42868c7c7d293950 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/Postprocessing.lean | Postprocessing | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "privPostPocess_DP_pre_reduct",
"depth": 1,
"n_commands": 0,
"n_lines": 276,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n\n -- By absolute continuity, nq1 is nonzero\n have Hnql1 : (∀ (u : U), nq l₂ u ≠ 0) := by\n rw [AbsCts] ... | [
{
"name": "rpow_nonzero",
"text": "lemma rpow_nonzero (x : ENNReal) (y : ℝ) (H : ¬(x = 0 ∧ 0 < y ∨ x = ⊤ ∧ y < 0)) : x ^ y ≠ 0 := by\n intro Hk\n apply H\n apply (ENNReal.rpow_eq_zero_iff).mp\n apply Hk\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 182,
"n_subproofs": 0,
"n_tactics": 5... | [
{
"name": "privPostPocess_DP_pre",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 89,
"n_chars": 3186,
"n_subproofs": 6,
"n_tactics": 75,
"cyclomatic": 3,
"n_automation": 18,
"n_rewrites": 9,
"n_structural": 25,
"automation_only": false,
"... | 4 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# Postprocessing
This file proves... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# Postprocessing
This file proves... | @@ -62,6 +62,12 @@
rw [lt_top_iff_ne_top]
trivial
+lemma rpow_nonzero (x : ENNReal) (y : ℝ) (H : ¬(x = 0 ∧ 0 < y ∨ x = ⊤ ∧ y < 0)) : x ^ y ≠ 0 := by
+ intro Hk
+ apply H
+ apply (ENNReal.rpow_eq_zero_iff).mp
+ apply Hk
+
/--
Jensen's inequality for privPostProcess, restructed to types where ``nq l₁`` is n... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b033140d58d1_4 | 2bd94bad43466b6b | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/Postprocessing.lean | Postprocessing | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "privPostPocess_DP_pre_reduct",
"depth": 1,
"n_commands": 0,
"n_lines": 276,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n\n -- By absolute continuity, nq1 is nonzero\n have Hnql1 : (∀ (u : U), nq l₂ u ≠ 0) := by\n rw [AbsCts] ... | [
{
"name": "rpow_nonzero",
"text": "lemma rpow_nonzero (x : ENNReal) (y : ℝ) (H : ¬(x = 0 ∧ 0 < y ∨ x = ⊤ ∧ y < 0)) : x ^ y ≠ 0 := by\n intro Hk\n apply H\n apply (ENNReal.rpow_eq_zero_iff).mp\n apply Hk\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 182,
"n_subproofs": 0,
"n_tactics": 5... | [
{
"name": "privPostProcess_zCDPBound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 43,
"n_chars": 1095,
"n_subproofs": 1,
"n_tactics": 36,
"cyclomatic": 5,
"n_automation": 6,
"n_rewrites": 9,
"n_structural": 14,
"automation_only": false,
... | 5 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# Postprocessing
This file proves... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# Postprocessing
This file proves... | @@ -62,6 +62,12 @@
rw [lt_top_iff_ne_top]
trivial
+lemma rpow_nonzero (x : ENNReal) (y : ℝ) (H : ¬(x = 0 ∧ 0 < y ∨ x = ⊤ ∧ y < 0)) : x ^ y ≠ 0 := by
+ intro Hk
+ apply H
+ apply (ENNReal.rpow_eq_zero_iff).mp
+ apply Hk
+
/--
Jensen's inequality for privPostProcess, restructed to types where ``nq l₁`` is n... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b033140d58d1_5 | 3a3bbbf56f12bd44 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/Postprocessing.lean | Postprocessing | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "privPostPocess_DP_pre",
"depth": 1,
"n_commands": 0,
"n_lines": 75,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Restruct the sum to a type where nq l₁ is nonzero\n have HSup1 (x : V) : Function.support (fun (a : U) => if x =... | [
{
"name": "privPostPocess_DP_pre_reduct",
"text": "/--\nJensen's inequality for privPostProcess, restructed to types where ``nq l₁`` is nonzero\n-/\ntheorem privPostPocess_DP_pre_reduct {U : Type} [m2 : MeasurableSpace U] [count : Countable U] [disc : DiscreteMeasurableSpace U] [Inhabited U]\n {nq : List T... | [
{
"name": "privPostProcess_zCDP",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 13,
"n_chars": 333,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_n... | 6 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# Postprocessing
This file proves... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.DifferentialPrivacy.Generic
import SampCert.DifferentialPrivacy.ZeroConcentrated.DP
/-!
# Postprocessing
This file proves... | @@ -68,6 +68,294 @@
apply (ENNReal.rpow_eq_zero_iff).mp
apply Hk
+/--
+Jensen's inequality for privPostProcess, restructed to types where ``nq l₁`` is nonzero
+-/
+theorem privPostPocess_DP_pre_reduct {U : Type} [m2 : MeasurableSpace U] [count : Countable U] [disc : DiscreteMeasurableSpace U] [Inhabited U]
+ {... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cf459962539a_0 | 0fe20caab9885846 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Uniform/Properties.lean | Properties | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "rw_ite",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n split\n rw [UniformPowerOfTwoSample_apply]\n simp only [PNat.mul_coe, one_div]\n apply double_large_enough\n trivial\n trivial"... | [
{
"name": "double_large_enough",
"text": "/--\nThe sample space of ``uniformP2 (2*n)`` is large enough to fit the sample\nspace for ``uniform(n)``.\n-/\n@[simp]\nlemma double_large_enough (n : PNat) (x : Nat) (support : x < n) :\n x < 2 ^ (log 2 ↑(2 * n)) := by\n have A : ∀ m : ℕ, m < 2 ^ (log 2 ↑(2 * m))... | [
{
"name": "rw_ite",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 19,
"n_chars": 551,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
}... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import Mathlib.Data.ENNReal.Basic
import SampCert.Samplers.Uniform.Code
/-!
# ``UniformSample`` Properti... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import Mathlib.Data.ENNReal.Basic
import SampCert.Samplers.Uniform.Code
/-!
# ``UniformSample`` Properti... | @@ -50,6 +50,25 @@
simp
/--
+The sample space of ``uniformP2 (2*n)`` is large enough to fit the sample
+space for ``uniform(n)``.
+-/
+@[simp]
+lemma double_large_enough (n : PNat) (x : Nat) (support : x < n) :
+ x < 2 ^ (log 2 ↑(2 * n)) := by
+ have A : ∀ m : ℕ, m < 2 ^ (log 2 ↑(2 * m)) := by
+ intro m
+ ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cf459962539a_1 | bc435f25b314ab23 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Uniform/Properties.lean | Properties | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "uniformPowerOfTwoSample_autopilot",
"depth": 1,
"n_commands": 0,
"n_lines": 28,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have X : (∑' (i : ℕ), if decide (↑n ≤ i) = true then UniformPowerOfTwoSample (2 * n) i else 0) +\n (∑... | [
{
"name": "tsum_comp",
"text": "lemma tsum_comp (n : PNat) :\n (∑' (x : ↑{i : ℕ | decide (↑n ≤ i) = true}ᶜ), (fun i => UniformPowerOfTwoSample (2 * n) i) ↑x)\n = ∑' (i : ↑{i : ℕ| decide (↑n ≤ i) = false}), UniformPowerOfTwoSample (2 * n) ↑i := by\n apply tsum_congr_set_coe\n simp\n ext x\n simp\n\n\... | [
{
"name": "uniformPowerOfTwoSample_autopilot",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 32,
"n_chars": 1402,
"n_subproofs": 6,
"n_tactics": 28,
"cyclomatic": 1,
"n_automation": 6,
"n_rewrites": 7,
"n_structural": 1,
"automation_only": fa... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import Mathlib.Data.ENNReal.Basic
import SampCert.Samplers.Uniform.Code
/-!
# ``UniformSample`` Properti... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import Mathlib.Data.ENNReal.Basic
import SampCert.Samplers.Uniform.Code
/-!
# ``UniformSample`` Properti... | @@ -86,11 +86,34 @@
trivial
-- Inline?
+lemma tsum_comp (n : PNat) :
+ (∑' (x : ↑{i : ℕ | decide (↑n ≤ i) = true}ᶜ), (fun i => UniformPowerOfTwoSample (2 * n) i) ↑x)
+ = ∑' (i : ↑{i : ℕ| decide (↑n ≤ i) = false}), UniformPowerOfTwoSample (2 * n) ↑i := by
+ apply tsum_congr_set_coe
+ simp
+ ext x
+ simp
+
... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cf459962539a_2 | a540820b3826b011 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Uniform/Properties.lean | Properties | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "UniformSample_apply",
"depth": 1,
"n_commands": 0,
"n_lines": 61,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [UniformSample, Bind.bind, Pure.pure, SLang.bind_apply, probUntil_apply,\n decide_eq_true_eq, rw_ite, one... | [
{
"name": "rw2",
"text": "theorem rw2 (n : PNat) : ((↑↑n)⁻¹ : ENNReal) = ((↑↑n)⁻¹ : NNReal) := by\n simp\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 94,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automat... | [
{
"name": "UniformSample_apply",
"fan_in": 2,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 68,
"n_chars": 2123,
"n_subproofs": 2,
"n_tactics": 61,
"cyclomatic": 7,
"n_automation": 11,
"n_rewrites": 11,
"n_structural": 4,
"automation_only": false,
"ma... | 6 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import Mathlib.Data.ENNReal.Basic
import SampCert.Samplers.Uniform.Code
/-!
# ``UniformSample`` Properti... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import Mathlib.Data.ENNReal.Basic
import SampCert.Samplers.Uniform.Code
/-!
# ``UniformSample`` Properti... | @@ -46,6 +46,9 @@
ofNat_ne_top, log_eq_zero_iff, ofNat_pos, mul_lt_iff_lt_one_right, lt_one_iff,
PNat.ne_zero, not_ofNat_le_one, or_self, and_true]
+theorem rw2 (n : PNat) : ((↑↑n)⁻¹ : ENNReal) = ((↑↑n)⁻¹ : NNReal) := by
+ simp
+
/--
The sample space of ``uniformP2 (2*n)`` is large enough to fit the samp... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cf459962539a_3 | 608cf7d92e09583f | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Uniform/Properties.lean | Properties | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "UniformSample_apply",
"depth": 1,
"n_commands": 0,
"n_lines": 61,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [UniformSample, Bind.bind, Pure.pure, SLang.bind_apply, probUntil_apply,\n decide_eq_true_eq, rw_ite, one... | [
{
"name": "rw_ite",
"text": "/--\nSimplify a ``uniformPowerOfTwoSample`` when guarded to be within the support.\n\nNote that the support of ``uniformPowerOfTwoSample`` (namely ``[0, 2 ^ log 2 (2 * n))``) is\nlarger than support restriction ``[0, n)`` imposed by the guard.\n-/\n@[simp]\nlemma rw_ite (n : PNa... | [
{
"name": "UniformSample_normalizes",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 9,
"n_lines": 11,
"n_chars": 308,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"m... | 9 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import Mathlib.Data.ENNReal.Basic
import SampCert.Samplers.Uniform.Code
/-!
# ``UniformSample`` Properti... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import Mathlib.Data.ENNReal.Basic
import SampCert.Samplers.Uniform.Code
/-!
# ``UniformSample`` Properti... | @@ -68,6 +68,24 @@
exact H1
exact Nat.lt_trans support (A ↑n)
+/--
+Simplify a ``uniformPowerOfTwoSample`` when guarded to be within the support.
+
+Note that the support of ``uniformPowerOfTwoSample`` (namely ``[0, 2 ^ log 2 (2 * n))``) is
+larger than support restriction ``[0, n)`` imposed by the guard.
+... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cf459962539a_4 | 26c4eaeee8c6ce58 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/Uniform/Properties.lean | Properties | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "rw_ite",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n split\n rw [UniformPowerOfTwoSample_apply]\n simp only [PNat.mul_coe, one_div]\n apply double_large_enough\n trivial\n trivial"... | [
{
"name": "double_large_enough",
"text": "/--\nThe sample space of ``uniformP2 (2*n)`` is large enough to fit the sample\nspace for ``uniform(n)``.\n-/\n@[simp]\nlemma double_large_enough (n : PNat) (x : Nat) (support : x < n) :\n x < 2 ^ (log 2 ↑(2 * n)) := by\n have A : ∀ m : ℕ, m < 2 ^ (log 2 ↑(2 * m))... | [
{
"name": "UniformSample_apply_ite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 12,
"n_chars": 362,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"ma... | 7 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import Mathlib.Data.ENNReal.Basic
import SampCert.Samplers.Uniform.Code
/-!
# ``UniformSample`` Properti... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import Mathlib.Data.ENNReal.Basic
import SampCert.Samplers.Uniform.Code
/-!
# ``UniformSample`` Properti... | @@ -50,6 +50,25 @@
simp
/--
+The sample space of ``uniformP2 (2*n)`` is large enough to fit the sample
+space for ``uniform(n)``.
+-/
+@[simp]
+lemma double_large_enough (n : PNat) (x : Nat) (support : x < n) :
+ x < 2 ^ (log 2 ↑(2 * n)) := by
+ have A : ∀ m : ℕ, m < 2 ^ (log 2 ↑(2 * m)) := by
+ intro m
+ ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1f586b2e5e21_0 | 5b1b027db8c2f8c9 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/ConcentratedBound.lean | ConcentratedBound | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "Renyi_divergence_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 192,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold RenyiDivergence'\n have A : 0 < 1 / (α - 1) := by\n simp [h']\n rw [← le_div_iff₀' A]\n refine Real.e... | [
{
"name": "sg_sum_pos'",
"text": "lemma sg_sum_pos' {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) (α : ℝ) :\n 0 < ((gauss_term_ℝ σ μ) x / ∑' (x : ℤ), (gauss_term_ℝ σ μ) x)^α := by\n apply rpow_pos_of_pos\n rw [div_pos_iff]\n left\n constructor\n · apply exp_pos\n · apply sum_gauss_term_pos h\n\n",
"fan_in": 1,
... | [
{
"name": "Renyi_divergence_bound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 200,
"n_chars": 5069,
"n_subproofs": 12,
"n_tactics": 189,
"cyclomatic": 3,
"n_automation": 13,
"n_rewrites": 83,
"n_structural": 40,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.DiscreteGaussian
import SampCert.Util.Gaussian.GaussBound
import SampCert.Util.Gaussian.GaussConvergence
impo... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.DiscreteGaussian
import SampCert.Util.Gaussian.GaussBound
import SampCert.Util.Gaussian.GaussConvergence
impo... | @@ -20,6 +20,15 @@
open Real Nat
+lemma sg_sum_pos' {σ : ℝ} (h : σ ≠ 0) (μ : ℝ) (α : ℝ) :
+ 0 < ((gauss_term_ℝ σ μ) x / ∑' (x : ℤ), (gauss_term_ℝ σ μ) x)^α := by
+ apply rpow_pos_of_pos
+ rw [div_pos_iff]
+ left
+ constructor
+ · apply exp_pos
+ · apply sum_gauss_term_pos h
+
/--
Real-valued Renyi Diverg... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1f586b2e5e21_1 | dafd2bf1bbd12636 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/ConcentratedBound.lean | ConcentratedBound | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "SG_Renyi_shift",
"depth": 1,
"n_commands": 0,
"n_lines": 108,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold RenyiDivergence'\n congr 2\n conv =>\n left\n arg 1\n ext x\n rw [SG_Renyi_simplify h]\n rw [divis... | [
{
"name": "SG_Renyi_simplify",
"text": "lemma SG_Renyi_simplify {σ : ℝ} (h : σ ≠ 0) (μ ν : ℤ) (α : ℝ) :\n (fun (x : ℤ) => (gauss_term_ℝ σ μ) x / ∑' (x : ℤ), (gauss_term_ℝ σ μ) x) x ^ α *\n (fun (x : ℤ) => (gauss_term_ℝ σ ν) x / ∑' (x : ℤ), (gauss_term_ℝ σ ν) x) x ^ (1 - α)\n = (gauss_term_ℝ σ μ) x ... | [
{
"name": "SG_Renyi_shift",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 112,
"n_chars": 3168,
"n_subproofs": 4,
"n_tactics": 101,
"cyclomatic": 1,
"n_automation": 10,
"n_rewrites": 41,
"n_structural": 17,
"automation_only": false,
"max_... | 2 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.DiscreteGaussian
import SampCert.Util.Gaussian.GaussBound
import SampCert.Util.Gaussian.GaussConvergence
impo... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.DiscreteGaussian
import SampCert.Util.Gaussian.GaussBound
import SampCert.Util.Gaussian.GaussConvergence
impo... | @@ -20,6 +20,60 @@
open Real Nat
+lemma SG_Renyi_simplify {σ : ℝ} (h : σ ≠ 0) (μ ν : ℤ) (α : ℝ) :
+ (fun (x : ℤ) => (gauss_term_ℝ σ μ) x / ∑' (x : ℤ), (gauss_term_ℝ σ μ) x) x ^ α *
+ (fun (x : ℤ) => (gauss_term_ℝ σ ν) x / ∑' (x : ℤ), (gauss_term_ℝ σ ν) x) x ^ (1 - α)
+ = (gauss_term_ℝ σ μ) x ^ α * (gauss_... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1f586b2e5e21_2 | 9845e389ca08f019 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/ConcentratedBound.lean | ConcentratedBound | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "SG_Renyi_shift",
"depth": 1,
"n_commands": 0,
"n_lines": 108,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold RenyiDivergence'\n congr 2\n conv =>\n left\n arg 1\n ext x\n rw [SG_Renyi_simplify h]\n rw [divis... | [
{
"name": "SG_Renyi_simplify",
"text": "lemma SG_Renyi_simplify {σ : ℝ} (h : σ ≠ 0) (μ ν : ℤ) (α : ℝ) :\n (fun (x : ℤ) => (gauss_term_ℝ σ μ) x / ∑' (x : ℤ), (gauss_term_ℝ σ μ) x) x ^ α *\n (fun (x : ℤ) => (gauss_term_ℝ σ ν) x / ∑' (x : ℤ), (gauss_term_ℝ σ ν) x) x ^ (1 - α)\n = (gauss_term_ℝ σ μ) x ... | [
{
"name": "Renyi_divergence_bound_pre",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 13,
"n_chars": 532,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
... | 5 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.DiscreteGaussian
import SampCert.Util.Gaussian.GaussBound
import SampCert.Util.Gaussian.GaussConvergence
impo... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.DiscreteGaussian
import SampCert.Util.Gaussian.GaussBound
import SampCert.Util.Gaussian.GaussConvergence
impo... | @@ -29,6 +29,60 @@
· apply exp_pos
· apply sum_gauss_term_pos h
+lemma SG_Renyi_simplify {σ : ℝ} (h : σ ≠ 0) (μ ν : ℤ) (α : ℝ) :
+ (fun (x : ℤ) => (gauss_term_ℝ σ μ) x / ∑' (x : ℤ), (gauss_term_ℝ σ μ) x) x ^ α *
+ (fun (x : ℤ) => (gauss_term_ℝ σ ν) x / ∑' (x : ℤ), (gauss_term_ℝ σ ν) x) x ^ (1 - α)
+ = ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1f586b2e5e21_3 | 404ab4d2f3512a4d | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/ConcentratedBound.lean | ConcentratedBound | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "SG_Renyi_shift",
"depth": 1,
"n_commands": 0,
"n_lines": 108,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold RenyiDivergence'\n congr 2\n conv =>\n left\n arg 1\n ext x\n rw [SG_Renyi_simplify h]\n rw [divis... | [
{
"name": "SG_Renyi_simplify",
"text": "lemma SG_Renyi_simplify {σ : ℝ} (h : σ ≠ 0) (μ ν : ℤ) (α : ℝ) :\n (fun (x : ℤ) => (gauss_term_ℝ σ μ) x / ∑' (x : ℤ), (gauss_term_ℝ σ μ) x) x ^ α *\n (fun (x : ℤ) => (gauss_term_ℝ σ ν) x / ∑' (x : ℤ), (gauss_term_ℝ σ ν) x) x ^ (1 - α)\n = (gauss_term_ℝ σ μ) x ... | [
{
"name": "Renyi_Gauss_divergence_bound'",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 8,
"n_lines": 82,
"n_chars": 3165,
"n_subproofs": 8,
"n_tactics": 72,
"cyclomatic": 2,
"n_automation": 10,
"n_rewrites": 18,
"n_structural": 25,
"automation_only": fal... | 8 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.DiscreteGaussian
import SampCert.Util.Gaussian.GaussBound
import SampCert.Util.Gaussian.GaussConvergence
impo... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.DiscreteGaussian
import SampCert.Util.Gaussian.GaussBound
import SampCert.Util.Gaussian.GaussConvergence
impo... | @@ -29,6 +29,60 @@
· apply exp_pos
· apply sum_gauss_term_pos h
+lemma SG_Renyi_simplify {σ : ℝ} (h : σ ≠ 0) (μ ν : ℤ) (α : ℝ) :
+ (fun (x : ℤ) => (gauss_term_ℝ σ μ) x / ∑' (x : ℤ), (gauss_term_ℝ σ μ) x) x ^ α *
+ (fun (x : ℤ) => (gauss_term_ℝ σ ν) x / ∑' (x : ℤ), (gauss_term_ℝ σ ν) x) x ^ (1 - α)
+ = ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1f586b2e5e21_4 | 31cfce3940655cd8 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/ZeroConcentrated/ConcentratedBound.lean | ConcentratedBound | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "Renyi_divergence_bound_pre",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold discrete_gaussian\n rw [SG_Renyi_shift h α μ ν (-ν)]\n rw [add_neg_cancel]\n apply Renyi_divergence_b... | [
{
"name": "Renyi_divergence_bound",
"text": "/--\nUpper bound on the Renyi Divergence between gaussians for any paramater `α > 1`.\n-/\ntheorem Renyi_divergence_bound {σ : ℝ} (h : σ ≠ 0) (μ : ℤ) (α : ℝ) (h' : 1 < α) :\n RenyiDivergence' (fun (x : ℤ) => (gauss_term_ℝ σ μ) x / ∑' x : ℤ, (gauss_term_ℝ σ μ) x)... | [
{
"name": "discrete_GaussianGenSample_ZeroConcentrated",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 9,
"n_lines": 65,
"n_chars": 2009,
"n_subproofs": 2,
"n_tactics": 61,
"cyclomatic": 7,
"n_automation": 13,
"n_rewrites": 24,
"n_structural": 22,
"automat... | 9 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.DiscreteGaussian
import SampCert.Util.Gaussian.GaussBound
import SampCert.Util.Gaussian.GaussConvergence
impo... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Util.Gaussian.DiscreteGaussian
import SampCert.Util.Gaussian.GaussBound
import SampCert.Util.Gaussian.GaussConvergence
impo... | @@ -89,6 +89,205 @@
noncomputable def RenyiDivergence' (p q : T → ℝ) (α : ℝ) : ℝ :=
(1 / (α - 1)) * Real.log (∑' x : T, (p x)^α * (q x)^(1 - α))
+/--
+Upper bound on the Renyi Divergence between gaussians for any paramater `α > 1`.
+-/
+theorem Renyi_divergence_bound {σ : ℝ} (h : σ ≠ 0) (μ : ℤ) (α : ℝ) (h' : 1 <... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_df85de6dea87_0 | 3063ebb75b940e54 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/DifferentialPrivacy/Queries/BoundedSum/Properties.lean | Properties | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "privNoisedBoundedSum_DP",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply dpn.noise_prop HP\n apply exactBoundedSum_sensitivity",
"n_chars": 65,
"n_subproofs": 0,
"n_tact... | [
{
"name": "exactBoundedSum_sensitivity",
"text": "/--\nSensitivity of the bounded sum is equal to the bound.\n-/\ntheorem exactBoundedSum_sensitivity (U : ℕ+) : sensitivity (exactBoundedSum U) U := by\n simp [sensitivity, exactBoundedSum]\n intros l₁ l₂ H\n have A : ∀ n : ℕ, (@min ℤ instMin (n : ℤ) (U : ... | [
{
"name": "privNoisedBoundedSum_DP",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 321,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Algebra.Group.Defs
import Init.Data.Int.Order
import SampCert.DifferentialPrivacy.Queries.BoundedSum.Code
/-!
# ``privNois... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import Mathlib.Algebra.Group.Defs
import Init.Data.Int.Order
import SampCert.DifferentialPrivacy.Queries.BoundedSum.Code
/-!
# ``privNois... | @@ -20,6 +20,40 @@
namespace SLang
+/--
+Sensitivity of the bounded sum is equal to the bound.
+-/
+theorem exactBoundedSum_sensitivity (U : ℕ+) : sensitivity (exactBoundedSum U) U := by
+ simp [sensitivity, exactBoundedSum]
+ intros l₁ l₂ H
+ have A : ∀ n : ℕ, (@min ℤ instMin (n : ℤ) (U : ℤ) = n) ∨ (@min ℤ ins... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_00654c838389_1 | 48777864f6acbad0 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/BernoulliNegativeExponential/Properties.lean | Properties | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 33 | 2 | [
{
"theorem_name": "adhoc'",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have C := @congrArg ℕ ENNReal (n - 2 + 1) (n - 1) Nat.cast (adhoc n h)\n simp at C\n trivial",
"n_chars": 101,
"n_subproo... | [
{
"name": "adhoc",
"text": "theorem adhoc (n : ℕ) (h : n > 1) :\n n - 2 + 1 = n - 1 := by\n rw [← tsub_tsub_assoc]\n · exact h\n · exact le.step le.refl\n\n",
"fan_in": 2,
"n_lines": 7,
"n_chars": 132,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
... | [
{
"name": "adhoc'",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 188,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
}
... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic
import SampCert.Samplers.... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic
import SampCert.Samplers.... | @@ -244,8 +244,17 @@
simp
rw [mul_assoc]
+theorem adhoc (n : ℕ) (h : n > 1) :
+ n - 2 + 1 = n - 1 := by
+ rw [← tsub_tsub_assoc]
+ · exact h
+ · exact le.step le.refl
+
theorem adhoc' (n : ℕ) (h : n > 1) :
- (n : ENNReal) - 2 + 1 = (n : ENNReal) - 1 := sorry
+ (n : ENNReal) - 2 + 1 = (n : ENNReal) - ... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_00654c838389_3 | 5dd7519eb38a9781 | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/BernoulliNegativeExponential/Properties.lean | Properties | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 33 | 2 | [
{
"theorem_name": "BernoulliExpNegSampleUnitAux_progress'",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have prog := BernoulliExpNegSampleUnitAux_progress num den (n - 2) 0 wf\n have A := nm2p2 n h\n r... | [
{
"name": "nm2p2",
"text": "theorem nm2p2 (n : ℕ) (h : n > 1) :\n n - 2 + 2 = n := by\n exact Nat.sub_add_cancel h\n\n-- Warning! BernoulliExpNegSampleUnitAux has a transition phase\n-- This min is suspicious: (min (fuel + 2) (fuel + k + 1) - 2)\n",
"fan_in": 2,
"n_lines": 7,
"n_chars": 217,
... | [
{
"name": "BernoulliExpNegSampleUnitAux_preservation'",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 24,
"n_chars": 1004,
"n_subproofs": 6,
"n_tactics": 19,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 7,
"n_structural": 1,
"automation_... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic
import SampCert.Samplers.... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic
import SampCert.Samplers.... | @@ -149,6 +149,12 @@
plus_two k 0 = k + 2 := by
simp [plus_two]
+theorem nm2p2 (n : ℕ) (h : n > 1) :
+ n - 2 + 2 = n := by
+ exact Nat.sub_add_cancel h
+
+-- Warning! BernoulliExpNegSampleUnitAux has a transition phase
+-- This min is suspicious: (min (fuel + 2) (fuel + k + 1) - 2)
@[simp]
theorem Bernoulli... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_00654c838389_4 | e8c7aeb087e49b9a | lean | lean | github.com/leanprover/SampCert | 6e2392c165652063fefc628d8f047b77ca393b0f | SampCert/Samplers/BernoulliNegativeExponential/Properties.lean | Properties | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 33 | 2 | [
{
"theorem_name": "gamma_extract",
"depth": 1,
"n_commands": 0,
"n_lines": 46,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have X : ∀ i : ℕ, (1 : ENNReal) + i ≠ 0 := by\n intro i\n simp\n have Y : ∀ i : ℕ, (1 : ENNReal) + i ≠ ⊤ := by\n i... | [
{
"name": "gamma_extract'",
"text": "theorem gamma_extract' (num : Nat) (den : PNat) (x : ENNReal) (h1 : x ≠ 0) (h2 : x ≠ ⊤) :\n ((num : ENNReal) / (x * den)) = ((num : ENNReal) / (den : ENNReal)) * x⁻¹ := by\n simp [division_def]\n rw [mul_assoc]\n congr\n rw [mul_comm]\n refine (ENNReal.eq_inv_of_mu... | [
{
"name": "gamma_extract",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 50,
"n_chars": 1135,
"n_subproofs": 4,
"n_tactics": 46,
"cyclomatic": 4,
"n_automation": 8,
"n_rewrites": 16,
"n_structural": 7,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic
import SampCert.Samplers.... | /-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean-Baptiste Tristan
-/
import SampCert.Foundations.Basic
import SampCert.Samplers.Uniform.Basic
import SampCert.Samplers.Bernoulli.Basic
import SampCert.Samplers.... | @@ -477,9 +477,71 @@
rw [BernoulliExpNegSampleUnitAux_apply]
simp
+theorem gamma_extract' (num : Nat) (den : PNat) (x : ENNReal) (h1 : x ≠ 0) (h2 : x ≠ ⊤) :
+ ((num : ENNReal) / (x * den)) = ((num : ENNReal) / (den : ENNReal)) * x⁻¹ := by
+ simp [division_def]
+ rw [mul_assoc]
+ congr
+ rw [mul_comm]
+ re... | {
"repo": "SampCert",
"git_repo": "github.com/leanprover/SampCert",
"revision": "6e2392c165652063fefc628d8f047b77ca393b0f",
"lean_toolchain": "leanprover/lean4:v4.29.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
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