refactor(Probability/Process): rework predictable and progressive processes

[jvanwinden]

The purpose of this PR is to rework IsProgressive and ProgMeasurable to have a weak (i.e., Measurable) and strong (i.e., StronglyMeasurable) variant, so that they are more in line with Adapted/StronglyAdapted.

As a side effect, some lemmas can have certain typeclasses removed (which were previously needed to go back and forth between Measurable and StronglyMeasurable).

Zulip discussion at #Brownian motion > Adapted Filtrations for Markov Chains and Markov Processes

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[mathlib-bors]

This pull request is now in draft mode. No active bors state needed cleanup.

While this PR remains draft, bors will ignore commands on this PR. Mark it ready for review before using commands like bors r+ or bors try.

[github-actions]

PR summary 3853566136

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ IsStronglyPredictable
+ IsStronglyProgressive
+ IsStronglyProgressive.stoppedProcess
+ IsStronglyProgressive.stronglyAdapted_stoppedProcess
+ IsStronglyProgressive.stronglyMeasurable_stoppedProcess
+ StronglyAdapted.isStronglyProgressive_of_continuous
+ StronglyAdapted.isStronglyProgressive_of_discrete
+ iff_measurable_add_one
+ isStronglyProgressive
+ isStronglyProgressive_const
+ isStronglyProgressive_min_stopping_time
+ isStronglyProgressive_of_tendsto
+ isStronglyProgressive_of_tendsto'
+ measurable_inclusion_predictable
+ of_measurable_add_one
++- stronglyAdapted
- IsPredictable
- ProgMeasurable
- ProgMeasurable.stoppedProcess
- ProgMeasurable.stronglyAdapted_stoppedProcess
- ProgMeasurable.stronglyMeasurable_stoppedProcess
- StronglyAdapted.progMeasurable_of_continuous
- StronglyAdapted.progMeasurable_of_discrete
- adapted
- isPredictable_iff_measurable_add_one
- isPredictable_of_measurable_add_one
- progMeasurable
- progMeasurable_const
- progMeasurable_min_stopping_time
- progMeasurable_of_tendsto
- progMeasurable_of_tendsto'

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).

[jvanwinden]

WIP

[jvanwinden]

-WIP

[jvanwinden]

This PR is now ready for review. It includes the following changes:

• Rename ProgMeasurable to IsStronglyProgressive.
• Rename IsPredictable to IsStronglyPredictable.
• Generalize various proofs relating to predictability and progressive measurability to get rid of [SecondCountableTopology] and other unneeded typeclasses.
• Deprecate Predictable.stronglyAdapted (which does not make use of IsStronglyPredictable)

The intent is to introduce Measurable variants of IsStronglyProgressive and IsPredictable and duplicate the surrounding API in future PRs.