[Merged by Bors] - refactor(data/real/ennreal): golf, generalize #14996
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urkud
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## Add new lemmas * `ennreal.bit0_strict_mono`, `ennreal.bit0_injective`, `ennreal.bit0_lt_bit0`, `ennreal.bit0_le_bit0`, `ennreal.bit0_top`; * `ennreal.bit1_strict_mono`, `ennreal.bit1_injective`, `ennreal.bit1_lt_bit1`, `ennreal.bit1_le_bit1`, `ennreal.bit1_top`; * `ennreal.div_eq_inv_mul`, `ennreal.of_real_mul'`; * `filter.eventually.prod_nhds`. ## Generalize lemmas * Drop unneeded assumption in `real.to_nnreal_bit0` and `ennreal.of_real_bit0`. ## Rename lemmas * `ennreal.mul_div_cancel` → `ennreal.div_mul_cancel`, fixing a TODO; * `prod_is_open.mem_nhds` → `prod_mem_nhds`: there are no open sets in the statement. ## Other changes * Golf some proofs. * Avoid non-final `simp`s here and there. * Move `mul_inv_cancel` etc up to use them in other proofs. * Move some `to_nnreal` lemmas above `to_real` lemmas, use them in `to_real` lemmas. * Use `to_dual` in `order_iso.inv_ennreal`.
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Add new lemmas
ennreal.bit0_strict_mono,ennreal.bit0_injective,ennreal.bit0_lt_bit0,ennreal.bit0_le_bit0,ennreal.bit0_top;ennreal.bit1_strict_mono,ennreal.bit1_injective,ennreal.bit1_lt_bit1,ennreal.bit1_le_bit1,ennreal.bit1_top;ennreal.div_eq_inv_mul,ennreal.of_real_mul';filter.eventually.prod_nhds.Generalize lemmas
real.to_nnreal_bit0andennreal.of_real_bit0.Rename lemmas
ennreal.mul_div_cancel→ennreal.div_mul_cancel, fixing a TODO;prod_is_open.mem_nhds→prod_mem_nhds: there are no open sets in the statement.Other changes
simps here and there.mul_inv_canceletc up to use them in other proofs.to_nnreallemmas aboveto_reallemmas, use them into_reallemmas.to_dualinorder_iso.inv_ennreal.