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Commit 2023-05-15 19:52 0b9eaaa7

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chore(analysis/special_functions): split up pow.lean (#19006) This PR splits up the monster file analysis.special_functions.pow into the following 6 files:

  • pow_complex: definition of a ^ b for complex a, b and basic properties (179 lines)
  • pow_real: definition of a ^ b for real a, b & lemmas about order / monotonicity (641 lines)
  • pow_nnreal: definitions for nnreal and ennreal types (693 lines)
  • pow_asymptotics: limiting behaviour at infinity (282 lines)
  • pow_continuity: continuity properties (500 lines)
  • pow_tactic: extensions to positivity and norm_num for powers (209 lines) No code has been added or removed, only moved around, and the only changes outside these files are adjustments to imports.

Estimated changes

deleted theorem asymptotics.is_O.rpow
deleted theorem asymptotics.is_o.rpow
deleted theorem complex.abs_cpow_inv_nat
deleted theorem complex.abs_cpow_le
deleted theorem complex.abs_cpow_of_imp
deleted theorem complex.abs_cpow_real
deleted theorem complex.conj_cpow
deleted theorem complex.conj_cpow_eq_ite
deleted theorem complex.cpow_add
deleted theorem complex.cpow_conj
deleted theorem complex.cpow_def
deleted theorem complex.cpow_eq_pow
deleted theorem complex.cpow_eq_zero_iff
deleted theorem complex.cpow_int_cast
deleted theorem complex.cpow_mul
deleted theorem complex.cpow_nat_cast
deleted theorem complex.cpow_nat_inv_pow
deleted theorem complex.cpow_neg
deleted theorem complex.cpow_neg_one
deleted theorem complex.cpow_one
deleted theorem complex.cpow_sub
deleted theorem complex.cpow_two
deleted theorem complex.cpow_zero
deleted theorem complex.eq_zero_cpow_iff
deleted theorem complex.inv_cpow
deleted theorem complex.inv_cpow_eq_ite'
deleted theorem complex.inv_cpow_eq_ite
deleted theorem complex.is_O_cpow_rpow
deleted theorem complex.of_real_cpow
deleted theorem complex.one_cpow
deleted theorem complex.zero_cpow
deleted theorem complex.zero_cpow_eq_iff
deleted theorem continuous.const_cpow
deleted theorem continuous.cpow
deleted theorem continuous.rpow
deleted theorem continuous.rpow_const
deleted theorem continuous_at.const_cpow
deleted theorem continuous_at.cpow
deleted theorem continuous_at.rpow
deleted theorem continuous_at.rpow_const
deleted theorem continuous_at_const_cpow'
deleted theorem continuous_at_const_cpow
deleted theorem continuous_at_cpow
deleted theorem continuous_at_cpow_const
deleted theorem continuous_on.const_cpow
deleted theorem continuous_on.cpow
deleted theorem continuous_on.cpow_const
deleted theorem continuous_on.rpow
deleted theorem continuous_on.rpow_const
deleted theorem continuous_within_at.cpow
deleted theorem continuous_within_at.rpow
deleted theorem cpow_eq_nhds'
deleted theorem cpow_eq_nhds
deleted theorem ennreal.coe_mul_rpow
deleted theorem ennreal.coe_rpow_def
deleted theorem ennreal.inv_rpow
deleted theorem ennreal.mul_rpow_eq_ite
deleted theorem ennreal.one_le_rpow
deleted theorem ennreal.one_lt_rpow
deleted theorem ennreal.one_rpow
deleted theorem ennreal.rpow_add
deleted theorem ennreal.rpow_eq_pow
deleted theorem ennreal.rpow_eq_top_iff
deleted theorem ennreal.rpow_eq_zero_iff
deleted theorem ennreal.rpow_le_one
deleted theorem ennreal.rpow_le_rpow
deleted theorem ennreal.rpow_le_rpow_iff
deleted theorem ennreal.rpow_lt_one
deleted theorem ennreal.rpow_lt_rpow
deleted theorem ennreal.rpow_lt_rpow_iff
deleted theorem ennreal.rpow_mul
deleted theorem ennreal.rpow_nat_cast
deleted theorem ennreal.rpow_neg
deleted theorem ennreal.rpow_neg_one
deleted theorem ennreal.rpow_one
deleted theorem ennreal.rpow_pos
deleted theorem ennreal.rpow_sub
deleted theorem ennreal.rpow_two
deleted theorem ennreal.rpow_zero
deleted theorem ennreal.to_nnreal_rpow
deleted theorem ennreal.to_real_rpow
deleted theorem ennreal.top_rpow_def
deleted theorem ennreal.top_rpow_of_neg
deleted theorem ennreal.top_rpow_of_pos
deleted theorem ennreal.zero_rpow_def
deleted theorem ennreal.zero_rpow_of_neg
deleted theorem ennreal.zero_rpow_of_pos
deleted theorem filter.tendsto.const_cpow
deleted theorem filter.tendsto.cpow
deleted theorem filter.tendsto.nnrpow
deleted theorem filter.tendsto.rpow
deleted theorem filter.tendsto.rpow_const
deleted theorem is_o_log_rpow_at_top
deleted theorem is_o_log_rpow_nhds_zero
deleted theorem is_o_log_rpow_rpow_at_top
deleted theorem is_o_rpow_exp_at_top
deleted theorem nnreal.coe_rpow
deleted theorem nnreal.continuous_at_rpow
deleted theorem nnreal.div_rpow
deleted theorem nnreal.inv_rpow
deleted theorem nnreal.mul_rpow
deleted theorem nnreal.one_le_rpow
deleted theorem nnreal.one_lt_rpow
deleted theorem nnreal.one_rpow
deleted theorem nnreal.rpow_add'
deleted theorem nnreal.rpow_add
deleted theorem nnreal.rpow_eq_pow
deleted theorem nnreal.rpow_eq_rpow_iff
deleted theorem nnreal.rpow_eq_zero_iff
deleted theorem nnreal.rpow_inv_rpow_self
deleted theorem nnreal.rpow_le_one
deleted theorem nnreal.rpow_le_rpow
deleted theorem nnreal.rpow_le_rpow_iff
deleted theorem nnreal.rpow_lt_one
deleted theorem nnreal.rpow_lt_rpow
deleted theorem nnreal.rpow_lt_rpow_iff
deleted theorem nnreal.rpow_mul
deleted theorem nnreal.rpow_nat_cast
deleted theorem nnreal.rpow_neg
deleted theorem nnreal.rpow_neg_one
deleted theorem nnreal.rpow_one
deleted theorem nnreal.rpow_pos
deleted theorem nnreal.rpow_self_rpow_inv
deleted theorem nnreal.rpow_sub'
deleted theorem nnreal.rpow_sub
deleted theorem nnreal.rpow_two
deleted theorem nnreal.rpow_zero
deleted theorem nnreal.sqrt_eq_rpow
deleted theorem nnreal.zero_rpow
deleted theorem norm_num.cpow_neg
deleted theorem norm_num.cpow_pos
deleted theorem norm_num.ennrpow_neg
deleted theorem norm_num.ennrpow_pos
deleted theorem norm_num.nnrpow_neg
deleted theorem norm_num.nnrpow_pos
deleted theorem norm_num.rpow_neg
deleted theorem norm_num.rpow_pos
deleted theorem real.abs_rpow_le_abs_rpow
deleted theorem real.abs_rpow_of_nonneg
deleted theorem real.continuous_at_rpow
deleted theorem real.div_rpow
deleted theorem real.eq_zero_rpow_iff
deleted theorem real.exists_rat_pow_btwn
deleted theorem real.exp_mul
deleted theorem real.exp_one_rpow
deleted theorem real.inv_rpow
deleted theorem real.le_rpow_add
deleted theorem real.le_rpow_iff_log_le
deleted theorem real.le_rpow_of_log_le
deleted theorem real.log_rpow
deleted theorem real.lt_rpow_iff_log_lt
deleted theorem real.lt_rpow_of_log_lt
deleted theorem real.mul_rpow
deleted theorem real.norm_rpow_of_nonneg
deleted theorem real.one_le_rpow
deleted theorem real.one_lt_rpow
deleted theorem real.one_lt_rpow_iff
deleted theorem real.one_rpow
deleted theorem real.pow_nat_rpow_nat_inv
deleted theorem real.rpow_add'
deleted theorem real.rpow_add
deleted theorem real.rpow_add_int
deleted theorem real.rpow_add_nat
deleted theorem real.rpow_add_of_nonneg
deleted theorem real.rpow_add_one
deleted theorem real.rpow_def
deleted theorem real.rpow_def_of_neg
deleted theorem real.rpow_def_of_nonneg
deleted theorem real.rpow_def_of_nonpos
deleted theorem real.rpow_def_of_pos
deleted theorem real.rpow_div_two_eq_sqrt
deleted theorem real.rpow_eq_nhds_of_neg
deleted theorem real.rpow_eq_nhds_of_pos
deleted theorem real.rpow_eq_pow
deleted theorem real.rpow_int_cast
deleted theorem real.rpow_le_one
deleted theorem real.rpow_le_rpow
deleted theorem real.rpow_le_rpow_iff
deleted theorem real.rpow_left_inj_on
deleted theorem real.rpow_lt_one
deleted theorem real.rpow_lt_one_iff
deleted theorem real.rpow_lt_rpow
deleted theorem real.rpow_lt_rpow_iff
deleted theorem real.rpow_mul
deleted theorem real.rpow_nat_cast
deleted theorem real.rpow_nat_inv_pow_nat
deleted theorem real.rpow_neg
deleted theorem real.rpow_neg_one
deleted theorem real.rpow_one
deleted theorem real.rpow_pos_of_pos
deleted theorem real.rpow_sub'
deleted theorem real.rpow_sub
deleted theorem real.rpow_sub_int
deleted theorem real.rpow_sub_nat
deleted theorem real.rpow_sub_one
deleted theorem real.rpow_sum_of_nonneg
deleted theorem real.rpow_sum_of_pos
deleted theorem real.rpow_two
deleted theorem real.rpow_zero
deleted theorem real.sqrt_eq_rpow
deleted theorem real.zero_rpow
deleted theorem real.zero_rpow_eq_iff
deleted theorem real.zero_rpow_le_one
deleted theorem real.zero_rpow_nonneg
deleted theorem tendsto_rpow_at_top
deleted theorem tendsto_rpow_div
deleted theorem tendsto_rpow_div_mul_add
deleted theorem tendsto_rpow_neg_at_top
deleted theorem tendsto_rpow_neg_div
deleted theorem zero_cpow_eq_nhds
added theorem complex.conj_cpow
added theorem complex.cpow_add
added theorem complex.cpow_conj
added theorem complex.cpow_def
added theorem complex.cpow_eq_pow
added theorem complex.cpow_int_cast
added theorem complex.cpow_mul
added theorem complex.cpow_nat_cast
added theorem complex.cpow_neg
added theorem complex.cpow_neg_one
added theorem complex.cpow_one
added theorem complex.cpow_sub
added theorem complex.cpow_two
added theorem complex.cpow_zero
added theorem complex.inv_cpow
added theorem complex.one_cpow
added theorem complex.zero_cpow
added theorem continuous.const_cpow
added theorem continuous.cpow
added theorem continuous.rpow
added theorem continuous.rpow_const
added theorem continuous_at.cpow
added theorem continuous_at.rpow
added theorem continuous_at_cpow
added theorem continuous_on.cpow
added theorem continuous_on.rpow
added theorem cpow_eq_nhds'
added theorem cpow_eq_nhds
added theorem filter.tendsto.cpow
added theorem filter.tendsto.nnrpow
added theorem filter.tendsto.rpow
added theorem zero_cpow_eq_nhds
added theorem ennreal.coe_mul_rpow
added theorem ennreal.coe_rpow_def
added theorem ennreal.inv_rpow
added theorem ennreal.one_le_rpow
added theorem ennreal.one_lt_rpow
added theorem ennreal.one_rpow
added theorem ennreal.rpow_add
added theorem ennreal.rpow_eq_pow
added theorem ennreal.rpow_le_one
added theorem ennreal.rpow_le_rpow
added theorem ennreal.rpow_lt_one
added theorem ennreal.rpow_lt_rpow
added theorem ennreal.rpow_mul
added theorem ennreal.rpow_nat_cast
added theorem ennreal.rpow_neg
added theorem ennreal.rpow_neg_one
added theorem ennreal.rpow_one
added theorem ennreal.rpow_pos
added theorem ennreal.rpow_sub
added theorem ennreal.rpow_two
added theorem ennreal.rpow_zero
added theorem ennreal.to_nnreal_rpow
added theorem ennreal.to_real_rpow
added theorem ennreal.top_rpow_def
added theorem ennreal.zero_rpow_def
added theorem nnreal.coe_rpow
added theorem nnreal.div_rpow
added theorem nnreal.inv_rpow
added theorem nnreal.mul_rpow
added theorem nnreal.one_le_rpow
added theorem nnreal.one_lt_rpow
added theorem nnreal.one_rpow
added theorem nnreal.rpow_add'
added theorem nnreal.rpow_add
added theorem nnreal.rpow_eq_pow
added theorem nnreal.rpow_le_one
added theorem nnreal.rpow_le_rpow
added theorem nnreal.rpow_lt_one
added theorem nnreal.rpow_lt_rpow
added theorem nnreal.rpow_mul
added theorem nnreal.rpow_nat_cast
added theorem nnreal.rpow_neg
added theorem nnreal.rpow_neg_one
added theorem nnreal.rpow_one
added theorem nnreal.rpow_pos
added theorem nnreal.rpow_sub'
added theorem nnreal.rpow_sub
added theorem nnreal.rpow_two
added theorem nnreal.rpow_zero
added theorem nnreal.sqrt_eq_rpow
added theorem nnreal.zero_rpow
added theorem complex.abs_cpow_le
added theorem complex.abs_cpow_real
added theorem complex.of_real_cpow
added theorem real.div_rpow
added theorem real.eq_zero_rpow_iff
added theorem real.exp_mul
added theorem real.exp_one_rpow
added theorem real.inv_rpow
added theorem real.le_rpow_add
added theorem real.le_rpow_of_log_le
added theorem real.log_rpow
added theorem real.lt_rpow_of_log_lt
added theorem real.mul_rpow
added theorem real.one_le_rpow
added theorem real.one_lt_rpow
added theorem real.one_lt_rpow_iff
added theorem real.one_rpow
added theorem real.rpow_add'
added theorem real.rpow_add
added theorem real.rpow_add_int
added theorem real.rpow_add_nat
added theorem real.rpow_add_one
added theorem real.rpow_def
added theorem real.rpow_def_of_neg
added theorem real.rpow_def_of_pos
added theorem real.rpow_eq_pow
added theorem real.rpow_int_cast
added theorem real.rpow_le_one
added theorem real.rpow_le_rpow
added theorem real.rpow_le_rpow_iff
added theorem real.rpow_left_inj_on
added theorem real.rpow_lt_one
added theorem real.rpow_lt_one_iff
added theorem real.rpow_lt_rpow
added theorem real.rpow_lt_rpow_iff
added theorem real.rpow_mul
added theorem real.rpow_nat_cast
added theorem real.rpow_neg
added theorem real.rpow_neg_one
added theorem real.rpow_one
added theorem real.rpow_pos_of_pos
added theorem real.rpow_sub'
added theorem real.rpow_sub
added theorem real.rpow_sub_int
added theorem real.rpow_sub_nat
added theorem real.rpow_sub_one
added theorem real.rpow_sum_of_pos
added theorem real.rpow_two
added theorem real.rpow_zero
added theorem real.sqrt_eq_rpow
added theorem real.zero_rpow
added theorem real.zero_rpow_eq_iff
added theorem real.zero_rpow_le_one
added theorem real.zero_rpow_nonneg