feat(Data/Seq): coinductive predicates for sequences

[vasnesterov]

• Introduce All, Pairwise, AtLeastAsLongAs predicates for sequences along with their coinductive principles and basic lemmas about them.
• Prove eq_of_bisim' and eq_of_bisim_strong coinductive principles for equality.

All of these "coinductive principles" are stated in the form as similar as possible to inductive principles.

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I also added set_option linter.style.longFile 2000 in the beginning of Seq.lean, because I am not sure how to split this file.

• depends on: [Merged by Bors] - feat(Data/Seq): update and set operations for Seq #26120

This PR is necessary for a new tactic (#18486), which computes the asymptotics of real functions.

[github-actions]

messageFile.md

[github-actions]

PR summary 78dfb8f8dd

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ All
+ All.coind
+ All.cons
+ All.nil
+ All_cons_iff
+ All_get
+ All_mp
+ All_of_get
+ AtLeastAsLongAs
+ AtLeastAsLongAs.coind
+ AtLeastAsLongAs.cons
+ AtLeastAsLongAs.cons_elim
+ AtLeastAsLongAs.nil
+ AtLeastAsLongAs_map
+ Pairwise
+ Pairwise.coind
+ Pairwise.coind_trans
+ Pairwise.cons
+ Pairwise.cons_cons_of_trans
+ Pairwise.cons_elim
+ Pairwise.nil
+ Pairwise_cons_cons_head
+ Pairwise_cons_nil
+ Pairwise_drop
+ Pairwise_tail
+ cons_AtLeastAsLongAs_cons
+ drop_zero
+ eq_of_bisim'
+ eq_of_bisim_strong
+ map_All_iff
+ modify
+ modify_cons_succ
+ modify_cons_zero
+ modify_nil
+ set
+ set_All
+ set_cons_succ
+ set_cons_zero
+ set_dropn_stable_of_lt
+ set_get_of_not_terminated
+ set_get_of_terminated
+ set_get_stable
+ set_nil
+ take_All

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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Increase in tech debt: (relative, absolute) = (1.00, 0.50)

Current number	Change	Type
2	1	large files

Current commit 78dfb8f8dd
Reference commit 5f30136da7

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).

[leanprover-community-bot-assistant]

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

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• [Merged by Bors] - feat(Data/Seq): update and set operations for Seq #26120
  By Dependent Issues (🤖). Happy coding!

[vasnesterov]

This PR has been migrated to a fork-based workflow: #28874