Feat: formalise Erdős Problem 359 #620
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smmercuri
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Aug 27, 2025
smmercuri
reviewed
Aug 27, 2025
| Then $A$ is strictly increasing. -/ | ||
| @[category test, AMS 11] | ||
| theorem erdos_359.variants.strictMono_of_isGoodFor (A : ℕ → ℕ) (n : ℕ) (hA : IsGoodFor A n) : | ||
| StrictMono A := by |
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I don't think this is true given the definition of IsGoodFor for n > 1. For example, if n = 2, then A 0 = 2 and A 1 = 1. This assumption might need to go in the definition of IsGoodFor itself
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This is basically by definition now, so I'm not sure it warrants inclusion as a test. Proof:
intro a b hab
induction hab with
| refl => exact (hA.2 a).1.1
| step _ a_ih => exact a_ih.trans (hA.2 _).1.1
callesonne
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smmercuri
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| /-- The predicate that `A 0 = n` and for all `j`, `A (j + 1)` is the smallest natural number that | ||
| cannot be written as a sum of consecutive terms of `A 0, ..., A j` -/ |
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This no longer matches the formal statement, we should include that A (j + 1) is greater than A j (or equivalently that A is strict mono
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#511