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Commit 2021-01-02 10:18 afc3f03a

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feat(algebra/ordered_group): add linear_ordered_comm_group and linear_ordered_cancel_comm_monoid (#5286) We have linear_ordered_add_comm_group but we didn't have linear_ordered_comm_group. This PR adds it, as well as multiplicative versions of canonically_ordered_add_monoid, canonically_linear_ordered_add_monoid and linear_ordered_cancel_add_comm_monoid. I added multiplicative versions of the lemmas about these structures too. The motivation is that I want to slightly generalise the notion of a valuation. [ also random other bits of tidying which I noticed along the way (docstring fixes, adding norm_cast attributes) ].

Estimated changes

deleted theorem add_eq_zero_iff
added theorem bot_eq_one
deleted theorem bot_eq_zero
deleted theorem exists_pos_add_of_lt
added theorem exists_pos_mul_of_lt
deleted theorem le_add_left
deleted theorem le_add_right
deleted theorem le_iff_exists_add
added theorem le_iff_exists_mul
added theorem le_mul_left
added theorem le_mul_right
added theorem le_one_iff_eq
deleted theorem le_zero_iff_eq
deleted theorem max_add_add_left
deleted theorem max_add_add_right
deleted theorem max_le_add_of_nonneg
added theorem max_le_mul_of_one_le
added theorem max_mul_mul_left
added theorem max_mul_mul_right
deleted theorem min_add_add_left
deleted theorem min_add_add_right
deleted theorem min_le_add_of_nonneg_left
added theorem min_mul_mul_left
added theorem min_mul_mul_right
added theorem mul_eq_one_iff
added theorem one_le
added theorem one_lt_iff_ne_one
deleted theorem zero_le
deleted theorem zero_lt_iff_ne_zero