Corradi's intersection lemma

[z-tech]

Adds Corrádi's intersection lemma (1969): if A₁, …, Aₘ ⊆ A each have
size a and pairwise intersections of size at most b, then
m · (a² − b·|A|) ≤ |A| · (a − b). The proof is the standard
double-counting plus Cauchy–Schwarz on the cover-count function
x ↦ #{i | x ∈ Aᵢ}.

Reference: Jukna, Extremal Combinatorics (Springer, 2011), Lemma 5.5.

Both an integer form (corradi_card_le) and a real-valued form
(corradi_card_le_real) are provided; the latter avoids
Nat-subtraction caveats and matches the form used in the classical
Johnson bound on list-decoding radius in MDS codes.

Co-authored-by: Ziyi Guan <TODO - replace with github no reply email>
Co-authored-by: Ignacio Manzur <TODO - replace with github no reply email>

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AI disclosure. Portions of this file (Lean source and docstrings)
were drafted with Claude (Anthropic). The authors have reviewed the
proofs, verified they compile against current Mathlib master, and take
responsibility for the mathematical content.

[github-actions]

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[github-actions]

PR summary 84426b902a

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Combinatorics.SetFamily.Corradi (new file)	1071

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Declarations diff

+ corradi_card_le_real
+ corradi_mul_le
+ coverCount
+ sum_coverCount_eq_card_mul
+ sum_coverCount_eq_sum_card
+ sum_coverCount_sq_eq_sum_inter_card
+ sum_inter_card_le

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

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

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

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No changes to strong technical debt.

No changes to weak technical debt.