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Additions in RIneq and removal of Rpow_def
This PR is a prerequisite for more simplifications in the Reals sublibrary. In file Rdefinitions.v - added the definition of the `pow` function (see the `Rpow_def.v` entry) In file RIneq.v Many new lemmas. In general these offer: - results about subtraction and division: these were not present and one had to unfold `Rdiv` or `Rminus` and use results about `Rinv` or `Ropp` - finer control over the goal or hypotheses with common mathematical operations such as "move this term from left to right" - more results about sign of operations and more common inequalities Added lemmas : - `Rgt_le_trans` - `Rmult_neq_0_neq_0` as a shorter name for the very useful `Rmult_integral_contrapositive_currified` - new families `Rmult_3_perm_???` and `Rplus_3_perm_???` - `Rmult_4shift_r`, `Rmult_4shift_l`, `Rplus_4shift_l` and `Rplus_4shift_r` - `Rminus_def_comm` - `Rminus_opp_r` - `Rminus_minus_distr` - `Rminus_plus_r` - `Rminus_plus_l` - `Rminus_minus_opp_m` - `Rminus_minus_opp_r` - new families `R<pred>_<opp>_chsd_[lr][lr]` to "change the side of a term" in an equality or inequality. `<pred>` is one of `eq`, `le`, `lt`, `ge`, `gt` `<opp>` is one of `plus`, `minus`, `mult`, `div` first `l` or `r` is the place of the term we want to move in the left operand second `l` or `r` is the place were we want it in the second operand - `Rmult_inv_l_id_m` - `Rplus_le_gt_compat` - `Rplus_gt_le_compat` - `Rle_plus_nneg` - `Rle_plus_npos` - `Ropp_npos` - `Ropp_nneg` - `Rminus_le_swap` - `Rminus_le_compat_r` - `Rminus_le_reg_r` - `Rminus_lt_compat_r` - `Rminus_lt_reg_r` - `Rminus_le_lt_mono` - `Rminus_lt_le_mono` - `Rminus_lt_lt_mono` - `Rminus_le_le_mono` - `Rle_minus_le` - `Rmult_le_compat_reg_r` - `Rmult_le_contravar_npos` - `Rmult_lt_compat_neg_r` and `Rmult_lt_compat_neg_l` - `Rmult_lt_contravar_neg` - `Rmult_npos_lt_contravar` - `Rmult_nneg_nneg` and `Rmult_npos_npos` - `Rinv_nneg` and `Rinv_npos` - `Rmult_ge_reg_l` and `Rmult_ge_reg_r` - `Rmult_lt_reg_neg_l` and `Rmult_lt_reg_neg_r` - `Rmult_le_reg_neg_l` and `Rmult_le_reg_neg_r` - `Rmult_ge_reg_neg_l` and `Rmult_ge_reg_neg_r` - `Rinv_pos_lt_cancel` and `Rinv_neg_lt_cancel` - `Rinv_pos_le_cancel` and `Rinv_neg_le_cancel` - `Rdiv_def_comm` - `Rmult_div` - `Rdiv_mult_id_l` and `Rdiv_mult_id_r` - `Rdiv_opp_opp` - `Rdiv_minus_minus_sym` - `Rdiv_div_inv_m` and `Rdiv_div_inv_r` - `Rdiv_lt_compat_r` and `Rdiv_lt_reg_r` - `Rdiv_lt_reg_neg_r` and `Rdiv_lt_contravar_r` - `Rdiv_gt_compat_r` and `Rdiv_gt_reg_r` - `Rdiv_gt_reg_neg_r` and `Rdiv_gt_contravar_r` - `Rdiv_le_compat_r` and `Rdiv_le_reg_r` - `Rdiv_ge_compat_r` and `Rdiv_ge_reg_r` - `Rdiv_le_reg_neg_r` and `Rdiv_ge_reg_neg_r` - `Rdiv_le_contravar_r` - `Rdiv_nneg_le_contravar_l` - `Rdiv_pos_lt_compat_l` - `Rdiv_neg_lt_contravar_l` - `Rdiv_neg_lt_compat_l` - `Rdiv_pos_pos_lt_cancel` - `Rdiv_neg_neg_lt_cancel` - `Rdiv_pos_lt_swap` - `Rdiv_pos_nneg_le_swap` - `Rdiv_nneg_nneg` and `Rdiv_npos_npos` - `Rmult_m1_l` and `Rmult_m1_r` File Rpow_def.v - The file `Rpow_def.v` is removed. The definition of `pow` is now a part of `Rdefinitions.v` (this is to reduce the number of files in order to ease documentation) File Raxioms.v - `is_lower_bound` and `is_glb` added for symmetry - the `bound` predicate has been renamed `bounded_from_above` (hidden notation `bounded` added for backwards compatibility) Removed Rpow_def entry in doc/stdlib/index-list.html.template
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