feat(Dehn function): define Dehn functions

[homeowmorphism]

For a presentation P of a group G and a word w : FreeGroup α that evaluates to
the identity in G, the area of w is the least number of conjugates of relators and of
inverse relators whose product is w. The Dehn function of P is given by
n ↦ max {area w | w = 1 in G, ‖w‖ ≤ n}, where ‖w‖ is the length of w.

Notes:

• area takes values in ℕ∞; it is ⊤ exactly when w does not evaluate to the identity in G
  (there is then no product of conjugates equal to w), and finite otherwise. This mirrors
  SimpleGraph.edist, and keeps area w = 0 ↔ w = 1 rather than colliding with the junk value.
• FreeGroup.norm needs [DecidableEq α], so kerBall and dehn do too.

---

The definitions were discussed by humans, but Claude Fable was used to write a lot of the API lemmas.

[mathlib-bors]

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[github-actions]

PR summary c36365a63b

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.GroupTheory.Presentation (new file)	1204
Mathlib.Geometry.Group.DehnFunction (new file)	1209

---

Declarations diff (regex)

+ FreeGroup.finite_setOf_norm_le
+ Group.Generators
+ Group.Presentation
+ Group.fg_iff_nonempty_finite_generators
+ Group.isFinitelyPresented_iff_exists_finite_presentation
+ IsConjRelDecomp
+ IsConjRelDecomp.append
+ IsConjRelDecomp.area_le
+ IsConjRelDecomp.conj
+ IsConjRelDecomp.inv
+ IsConjRelDecomp.lift_eq_one
+ area
+ area_conj
+ area_conj_le
+ area_eq_iInf
+ area_eq_top_iff
+ area_eq_zero_iff
+ area_inv
+ area_inv_le
+ area_le_dehn
+ area_le_dehn_norm
+ area_le_one_of_mem_conjugatesOfSet_symmRel
+ area_le_one_of_mem_rel
+ area_le_one_of_mem_symmRel
+ area_mul_le
+ area_ne_top_iff
+ area_ne_top_of_mem_kerBall
+ area_one_eq_zero
+ dehn
+ dehn_le_iff
+ dehn_mono
+ dehn_zero
+ exists_isConjRelDecomp_iff_mem_ker
+ exists_isConjRelDecomp_length_eq_area
+ fg
+ inv_mem_conjugatesOfSet_symmRel
+ inv_mem_kerBall
+ inv_mem_symmRel
+ isConjRelDecomp_one_nil
+ isConjRelDecomp_singleton
+ isFinitelyPresented
+ kerBall
+ kerBall_finite
+ kerBall_mono
+ kerBall_nonempty
+ kerBall_subset_ker
+ kerBall_zero
+ ker_lift
+ lift
+ lift_eq_one_of_mem_conjugatesOfSet_symmRel
+ lift_eq_one_of_mem_rel
+ lift_eq_one_of_mem_symmRel
+ lift_of
+ lift_surjective
+ lift_surjective'
+ mem_kerBall
+ mem_kerBall_norm
+ mul_mem_kerBall
+ natCast_dehn
+ ofLiftSurjective
+ one_mem_kerBall
+ presentedGroupEquiv
+ presentedGroupEquiv_of
+ rel_subset_symmRel
+ sSup_area_image_kerBall_ne_top
+ self
+ symmRel
+ val_ofLiftSurjective
+ val_self
++ range_lift_eq_top

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.

Declarations diff (Lean -- pending)

Computed after the build finishes.

---

No changes to strong technical debt.

Increase in weak tech debt: (relative, absolute) = (2.00, 0.00)

Current number	Change	Type (weak)
5016	2	exposed public sections

Current commit c36365a63b
Reference commit 4608056c77

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/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).

[github-actions]

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• fix (bug fix)
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