[ refactor ] Restate, and use, the definitions of Monotonic etc. operations
#2580
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Thanks - these already are easier to understand. |
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How do I remove #1579 from the |
Not sure how you did it, but it's gone for me 🎉 |
| mono⇒cong sym reflexive antisym mono x≈y = antisym | ||
| (mono (reflexive x≈y)) | ||
| (mono (reflexive (sym x≈y))) | ||
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| antimono⇒cong : Symmetric ≈₁ → ≈₁ ⇒ ≤₁ → Antisymmetric ≈₂ ≤₂ → | ||
| ∀ {f} → f Preserves ≤₁ ⟶ (flip ≤₂) → f Preserves ≈₁ ⟶ ≈₂ | ||
| ∀ {f} → f Preserves ≤₁ ⟶ (flip ≤₂) → Monotonic₁ ≈₁ ≈₂ f |
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This unfortunately is stated so as not to be able to exploit the refactoring redefinition of Antitonic₁ in Relation.Binary.Definitions below (wrong relation gets flipped!). Downstream refactoring?
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Now that the abstract definitions are mostly in place, can look at the instantiations in |
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Remark: all of the |
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So this should now be ready, modulo:
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| *-monoʳ-≤ : ∀ n → (n *_) Preserves _≤_ ⟶ _≤_ | ||
| *-monoʳ-≤ n m≤o = *-mono-≤ (≤-refl {n}) m≤o | ||
| *-monoʳ-≤ : LeftMonotonic _≤_ _≤_ _*_ | ||
| *-monoʳ-≤ = mono₂⇒monoˡ {≤₁ = _≤_} {≤₂ = _≤_} {≤₃ = _≤_} ≤-refl *-mono-≤ |
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This providing of implicits is annoying. Suggests that some of them should be explicit in the proof?
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Yes, I've been scratching my head over how it might be avoided... without a conclusion yet.
| +-monoʳ-≤ : ∀ n → (n +_) Preserves _≤_ ⟶ _≤_ | ||
| +-monoʳ-≤ n m≤o = +-mono-≤ (≤-refl {n}) m≤o | ||
| +-monoʳ-≤ : LeftMonotonic _≤_ _≤_ _+_ | ||
| +-monoʳ-≤ = mono₂⇒monoˡ {≤₃ = _≤_} ≤-refl +-mono-≤ |
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I'll resolve the merge conflict later, meanwhile tricky questions above needing more thought... ;-)... so have converted back to DRAFT. |
Aim: towards tackling #1579
TODO:
Data.Nat.*UPDATED: unsolved metas suggest some more revision is necessary :-(Data.Integer.*Data.Rational.*breakingchanges (v3.0: separate PR once the rest is done?)