Odd powers of real numbers are strictly increasing #1737
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Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
src/real-numbers/pointwise-continuous-functions-real-numbers.lagda.md
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src/real-numbers/strictly-increasing-functions-real-numbers.lagda.md
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src/real-numbers/strictly-increasing-functions-real-numbers.lagda.md
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src/real-numbers/strictly-increasing-functions-real-numbers.lagda.md
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src/metric-spaces/pointwise-continuous-functions-metric-spaces.lagda.md
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fredrik-bakke
approved these changes
Dec 4, 2025
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Very nice work! My comments mostly regard naming of certain entries and file organization.
Co-authored-by: Fredrik Bakke <fredrbak@gmail.com>
| (f : type-function-Metric-Space X Y) | ||
| where | ||
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| is-pointwise-continuous-prop-function-Metric-Space : Prop (l1 ⊔ l2 ⊔ l4) |
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| is-pointwise-continuous-prop-function-Metric-Space : Prop (l1 ⊔ l2 ⊔ l4) | |
| is-pointwise-continuous-prop-map-Metric-Space : Prop (l1 ⊔ l2 ⊔ l4) |
| (f : type-function-Metric-Space X Y) | ||
| where | ||
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| is-classically-pointwise-continuous-prop-function-Metric-Space : |
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| is-classically-pointwise-continuous-prop-function-Metric-Space : | |
| is-classically-pointwise-continuous-prop-map-Metric-Space : |
| where | ||
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| abstract | ||
| is-pointwise-continuous-is-classically-pointwise-continuous-ACω-function-Metric-Space : |
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| is-pointwise-continuous-is-classically-pointwise-continuous-ACω-function-Metric-Space : | |
| is-pointwise-continuous-is-classically-pointwise-continuous-map-acω-Metric-Space : |
| (y : type-Metric-Space Y) | ||
| where | ||
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| is-classical-limit-prop-function-Metric-Space : Prop (l1 ⊔ l2 ⊔ l4) |
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| is-classical-limit-prop-function-Metric-Space : Prop (l1 ⊔ l2 ⊔ l4) | |
| is-classical-limit-prop-map-Metric-Space : Prop (l1 ⊔ l2 ⊔ l4) |
| where | ||
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| abstract | ||
| is-classical-limit-is-limit-function-Metric-Space : |
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| is-classical-limit-is-limit-function-Metric-Space : | |
| is-classical-limit-is-limit-map-Metric-Space : |
| where | ||
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| abstract | ||
| is-limit-is-classical-limit-ACω-function-Metric-Space : |
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| is-limit-is-classical-limit-ACω-function-Metric-Space : | |
| is-limit-is-classical-limit-map-acω-Metric-Space : |
| ( leq-right-min-ℚ⁺ (μf ε) (μg ε)) | ||
| ( Ncc')))) | ||
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| product-pointwise-continuous-map-Metric-Space : |
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| product-pointwise-continuous-map-Metric-Space : | |
| pointwise-continuous-map-product-Metric-Space : |
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compare to equiv-product. This should be seen as a functorial action of products.
| is-pointwise-continuous-is-isometry-Metric-Space X X id | ||
| ( is-isometry-id-Metric-Space X) | ||
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| pointwise-continuous-id-Metric-Space : |
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| pointwise-continuous-id-Metric-Space : | |
| id-pointwise-continuous-map-Metric-Space : |
| where | ||
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| abstract | ||
| is-pointwise-continuous-id-Metric-Space : |
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| is-pointwise-continuous-id-Metric-Space : | |
| is-pointwise-continuous-map-id-Metric-Space : |
| is-pointwise-continuous-is-short-function-Metric-Space X Y _ | ||
| ( is-short-constant-function-Metric-Space X Y y) | ||
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| pointwise-continuous-constant-function-Metric-Space : |
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const-pointwise-continuous-map
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please use the predefined const function in your definition
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Builds on some material from #1712 .