prove `WithTop` and `WithBot` theorems

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Post PR summary comment on: pull_request_target

post-or-update-summary-comment

continuous integration (mathlib forks) on: pull_request_target 2

ci (fork) / Build

ci (fork) / Lint style

ci (fork) / Test and lint

ci (fork) / Upload to cache

ci (fork) / Post-Build Step

ci (fork) / Post-CI job

Run pre-commit and in-place update PR on push on: pull_request 1

main

Commit Verification on: pull_request

Verify Transient and Automated Commits

lint and suggest on: pull_request 1

Lint and suggest

Label PR based on Comment on: pull_request_review

update-label

Bors merge/delegate follow-up on: pull_request_review

Detect bors merge/delegate command

bot fix style on: pull_request_review

Fix style issues from lint

Maintainer merge on: pull_request_review

Ping maintainers on Zulip