feat(Data/Nat/Find): Nat.find_mono_of_le and Nat.find_congr

[pechersky]

Both strong versions (p and q agree below some x) and weak (p and q agree everywhere)

helper for not juggling generalize_proofs

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[github-actions]

PR summary f22fa274d0

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ find_congr
+ find_congr'
+ find_mono_of_le

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[Ruben-VandeVelde]

Thanks, this seems reasonable.

maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by Ruben-VandeVelde.

[Vierkantor]

The declaration itself looks reasonable otherwise. Thanks!

bors d+

[mathlib-bors]

✌️ pechersky can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[eric-wieser]

Please update the PR description.

I claim that actually generalize_proofs probably was never needed, and simp_rw would have worked fine; but I don't know your original use case.

[pechersky]

I claim that actually generalize_proofs probably was never needed, and simp_rw would have worked fine; but I don't know your original use case.

You're right:

import Mathlib

attribute [local instance] PiNat.metricSpace

open PiNat

lemma foo (x y c : ℕ → ℕ) : firstDiff (x + c) (y + c) = firstDiff x y := by
  rw [firstDiff, firstDiff]
  rcases eq_or_ne x y with rfl|h
  · simp
  rw [dif_pos, dif_pos h]
  · congr -- you were right
    simp
  -- another option now
  -- · convert Nat.find_congr' _
  --   simp
  · simp [h]

lemma bar (x y c : ℕ → ℕ) : dist (x + c) (y + c) = dist x y := by
  rcases eq_or_ne x y with rfl|h
  · simp
  rw [dist_eq_of_ne, dist_eq_of_ne h]
  · simp [foo]
  · simp [h]