If q : ℚ is in the lower cut of a real, real-ℚ q is less than that real
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| @@ -235,6 +235,27 @@ module _ | |||
| tr (is-in-upper-cut-ℝ x) (inv (neg-neg-ℚ p)) p-in-ux)) | |||
| ``` | |||
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| ### If a rational `q` is in the lower cut of real `x`, `real-ℚ q < x` | |||
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| ### If a rational `q` is in the lower cut of real `x`, `real-ℚ q < x` | |
| ### If a rational is in the lower cut of `x`, then it is strictly less than `x` |
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| {l : Level} | ||
| (q : ℚ) | ||
| (x : ℝ l) |
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| {l : Level} | |
| (q : ℚ) | |
| (x : ℝ l) | |
| {l : Level} (q : ℚ) (x : ℝ l) |
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And the analogous statement for upper cuts.