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Commit 2020-09-03 17:36 2d40d9c6

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feat(data/padics): universal property of Z_p (#3950) We establish the universal property of $\mathbb{Z}_p$ as a projective limit. Given a family of compatible ring homs $f_k : R \to \mathbb{Z}/p^n\mathbb{Z}$, there is a unique limit $R \to \mathbb{Z}_p$. In addition, we:

  • split padic_integers.lean into two files, creating ring_homs.lean
  • renamings: padic_norm_z.* -> padic_int.norm_*

Estimated changes

deleted theorem padic_int.appr_lt
deleted theorem padic_int.appr_spec
modified theorem padic_int.coe_sub
modified theorem padic_int.ext
deleted theorem padic_int.is_unit_denom
deleted theorem padic_int.ker_to_zmod
deleted theorem padic_int.ker_to_zmod_pow
deleted def padic_int.mod_part
deleted theorem padic_int.mod_part_lt_p
deleted theorem padic_int.mod_part_nonneg
added theorem padic_int.norm_def
added theorem padic_int.norm_le_one
added theorem padic_int.norm_mul
added theorem padic_int.norm_one
added theorem padic_int.norm_p
added theorem padic_int.norm_p_pow
added theorem padic_int.norm_pow
modified theorem padic_int.pow_p_dvd_int_iff
deleted def padic_int.to_zmod
deleted theorem padic_int.to_zmod_spec
deleted def padic_int.zmod_repr
deleted theorem padic_int.zmod_repr_lt_p
deleted theorem padic_int.zmod_repr_spec
deleted theorem padic_norm_z.le_one
deleted theorem padic_norm_z.mul
deleted theorem padic_norm_z.norm_one
deleted theorem padic_norm_z.norm_p
deleted theorem padic_norm_z.norm_p_pow
deleted theorem padic_norm_z.one
deleted theorem padic_norm_z.pow
deleted theorem padic_norm_z
added theorem padic_int.appr_lt
added theorem padic_int.appr_mono
added theorem padic_int.appr_spec
added theorem padic_int.ker_to_zmod
added def padic_int.lift
added theorem padic_int.lift_self
added theorem padic_int.lift_spec
added theorem padic_int.lift_unique
added theorem padic_int.nth_hom_zero
added theorem padic_int.to_zmod_spec