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Commit 2022-11-30 13:42 83871f6c

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chore(data/real/ereal): fix addition and multiplication on ereal (#17770) The current version of multiplication on ereal is completely broken (it satisfies (-1) * (+∞) = +∞). The addition is not really broken, but it satisfies (-∞) + (+∞) = +∞, while the analogy with ennreal through the exponential and the logarithm suggest that a better convention would be (-∞) + (+∞) = -∞. We fix the multiplication (by defining one directly by hand) and tweak the addition to obey the better convention (by changing the definition from with_top (with_bot ℝ) to with_bot (with_top ℝ)).

Estimated changes

added theorem ereal.abs_bot
added theorem ereal.abs_coe_lt_top
added theorem ereal.abs_eq_zero_iff
added theorem ereal.abs_mul
added theorem ereal.abs_top
added theorem ereal.abs_zero
added theorem ereal.add_bot
added theorem ereal.add_eq_bot_iff
deleted theorem ereal.add_eq_top_iff
added theorem ereal.add_lt_top
deleted theorem ereal.add_lt_top_iff
deleted theorem ereal.add_top
added theorem ereal.bot_add
deleted theorem ereal.bot_add_bot
deleted theorem ereal.bot_add_coe
added theorem ereal.bot_lt_add_iff
modified theorem ereal.bot_lt_coe
modified theorem ereal.bot_mul_bot
deleted theorem ereal.bot_mul_coe
added theorem ereal.bot_mul_of_neg
added theorem ereal.bot_mul_of_pos
added theorem ereal.bot_mul_top
added theorem ereal.bot_sub
deleted theorem ereal.bot_sub_coe
deleted theorem ereal.bot_sub_top
deleted theorem ereal.coe_add_bot
added theorem ereal.coe_add_top
modified theorem ereal.coe_ennreal_add
modified theorem ereal.coe_lt_top
modified theorem ereal.coe_mul
deleted theorem ereal.coe_mul_bot
modified theorem ereal.coe_sub_bot
added theorem ereal.mul_bot_of_neg
added theorem ereal.mul_bot_of_pos
deleted theorem ereal.mul_top
added theorem ereal.mul_top_of_neg
added theorem ereal.mul_top_of_pos
added theorem ereal.sign_bot
added theorem ereal.sign_coe
added theorem ereal.sign_mul
added theorem ereal.sign_top
deleted theorem ereal.sub_bot
added theorem ereal.sub_top
modified theorem ereal.to_real_mul
deleted theorem ereal.top_add
added theorem ereal.top_add_coe
added theorem ereal.top_add_top
deleted theorem ereal.top_mul
added theorem ereal.top_mul_bot
added theorem ereal.top_mul_of_neg
added theorem ereal.top_mul_of_pos
added theorem ereal.top_mul_top
deleted theorem ereal.top_sub
added theorem ereal.top_sub_bot
added theorem ereal.top_sub_coe
modified def ereal