[Merged by Bors] - feat(set_theory/surreal/dyadic): define add_monoid_hom structure on dyadic map #11052
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src/set_theory/surreal/dyadic.lean
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| ... = a • pow_half b' + c • pow_half d' : add_comm _ _, | ||
| end } | ||
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| lemma dyadic_map_apply (m : ℤ) (p : submonoid.powers (2 : ℤ)) : |
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Thanks, I added it.
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It needed converting into simp normal form.
@[simp] lemma dyadic_map_apply (m : ℤ) (p : submonoid.powers (2 : ℤ)) :
dyadic_map (is_localization.mk' (localization (submonoid.powers 2)) m p) =
m • pow_half (submonoid.log p) 
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| @@ -234,8 +236,8 @@ lemma pow_right_injective_iff_pow_injective {n : M} : | |||
| function.injective (λ m : ℕ, n ^ m) ↔ function.injective (pow n) := | |||
| subtype.coe_injective.of_comp_iff (pow n) | |||
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| theorem log_pow_eq_self [decidable_eq M] {n : M} (h : function.injective (λ m : ℕ, n ^ m)) (m : ℕ) : | |||
| log (pow n m) = m := | |||
| @[simp] theorem log_pow_eq_self [decidable_eq M] {n : M} (h : function.injective (λ m : ℕ, n ^ m)) | |||
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Do we have simp lemmas that prove h?
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h isn't always true though. The closest we have are int.pow_right_injective and nat.pow_right_injective.
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…yadic map (#11052) The proof is mechanical and mostly requires unraveling definitions. The above map cannot be extended to ring morphism as so far there's not multiplication structure on surreal numbers.
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The proof is mechanical and mostly requires unraveling definitions.
The above map cannot be extended to ring morphism as so far there's not multiplication structure on surreal numbers.