feat: birthday of Dyadic.toIGame x - #428
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vihdzp
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Long proofs, will check tomorrow...
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I think you can isolate the following lemma: if x.den ≠ 1, then max x.lower.birthday x.upper.birthday + 1 = x.birthday.
This lemma should follow from the following: either x.lower.num.natAbs / x.lower.den = x.num.natAbs / x.den, or x.lower.den = 1. Same for upper.
Basically, I think you should split up this big proof into a bunch of other, less big proofs.
Co-authored-by: Violeta Hernández Palacios <vi.hdz.p@gmail.com>
Co-authored-by: Violeta Hernández Palacios <vi.hdz.p@gmail.com>
Co-authored-by: Violeta Hernández Palacios <vi.hdz.p@gmail.com>
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I don't have any substantial golfs here. Working with rational numbers just kind of sucks, doesn't it?
| unfold Dyadic.den at hx ⊢ | ||
| rw [coe_lower, coe_upper] | ||
| unfold Dyadic.den | ||
| rw [Rat.sub_def', Rat.den_mkRat, if_neg (by positivity), |
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I think you can further extract den_lower and den_upper lemmas out of this big rw chain.
Co-authored-by: Violeta Hernández Palacios <vi.hdz.p@gmail.com>
Co-authored-by: Violeta Hernández Palacios <vi.hdz.p@gmail.com>
Co-authored-by: Violeta Hernández Palacios <vi.hdz.p@gmail.com>
Co-authored-by: Violeta Hernández Palacios <vi.hdz.p@gmail.com>
Co-authored-by: Violeta Hernández Palacios <vi.hdz.p@gmail.com>
vihdzp
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Sep 12, 2026
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Give an explicit formula for
Dyadic.toIGame x. Note that the formula given in theproof_wantedis wrong.birthday_intCast#426