feat(Combinatorics/SimpleGraph): hamiltonians graphs don't contain bridges

[YaelDillies]

Replace the longer proof which further assumed that the vertex set has at least three elements.

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• depends on: [Merged by Bors] - refactor(Combinatorics/SimpleGraph): make the vertex argument explicit in Walk.rotate #36800

[github-actions]

PR summary 88d1cd4b99

Import changes exceeding 2%

%	File
+29.97%	Mathlib.Combinatorics.SimpleGraph.Hamiltonian

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Combinatorics.SimpleGraph.Hamiltonian	594	772	+178 (+29.97%)

Import changes for all files

Files	Import difference
Mathlib.Combinatorics.SimpleGraph.Hamiltonian	178

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Declarations diff

+ IsBridge.nontrivial
+ IsBridge.not_isHamiltonian
+ IsCircuit.of_rotate
+ IsCycle.of_rotate
+ IsHamiltonian.exists_isHamiltonianCycle
+ IsHamiltonian.finite
+ IsHamiltonianCycle.finite
+ IsHamiltonianCycle.of_rotate
+ IsHamiltonianCycle.rotate
+ IsTrail.isEdgeReachable_two
+ IsTrail.isEdgeReachable_two_of_isEdgeReachable_two
+ IsTrail.isEdgeReachable_two_of_isEdgeReachable_two_aux
+ IsTrail.of_rotate
+ isCircuit_rotate
+ isCycle_rotate
+ isHamiltonianCycle_rotate
+ isTrail_rotate
+ length_rotate
+ not_isHamiltonianCycle_of_infinite
+ not_isHamiltonian_of_infinite
+ rotate_eq_nil
- IsTrail.not_mem_edges_of_not_isEdgeReachable_two
- not_isHamiltonian_of_isBridge

You can run this locally as follows

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

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

The doc-module for scripts/pr_summary/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/reporting/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).

[mathlib-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - refactor(Combinatorics/SimpleGraph): make the vertex argument explicit in Walk.rotate #36800
  By Dependent Issues (🤖). Happy coding!

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.