feat: port algebra/stepindex.v#515
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Description
Port
algebra/stepindex.v. It will be nice to have this ready before moving ontoalgebra/stepindex_finite.vas the latter requires refactoring a large number of files.Addresses #203.
The current implementation defines
SIdxas a type class that extendsLT,LEandZerofromInit.Preludeso that we can reuse the notations<,≤and0. Meanwhile,succᵢis a notation defined on our own.Checklist of definitions and theorems
SIdx.caseSIdx.eq_decSIdx.inhabitedSIdx.le_0_lSIdx.le_0_rSIdx.le_decSIdx.le_gt_casesSIdx.le_lt_transSIdx.le_lteq(ignored)SIdx.le_neqSIdx.le_ngtSIdx.le_poSIdx.le_succ_diag_rSIdx.le_succ_lSIdx.le_succ_l_2(ignored)SIdx.le_totalSIdx.limitSIdx.limit_0SIdx.limit_SSIdx.limit_finiteSIdx.limit_lt_0SIdx.lt_decSIdx.lt_ge_casesSIdx.lt_le_inclSIdx.lt_le_transSIdx.lt_ngeSIdx.lt_strictSIdx.lt_succ_diag_r(ignored)SIdx.lt_succ_diag_r'SIdx.lt_succ_rSIdx.lt_trans(ignored)SIdx.lt_trichotomy(ignored)SIdx.lt_wf(ignored)SIdx.neq_0_lt_0SIdx.neq_succ_0SIdx.nlt_0_r(ignored)SIdx.nlt_succ_rSIdx.recSIdx.rec_limSIdx.rec_lim_ext(ignored)SIdx.rec_succSIdx.rec_unfoldSIdx.rec_zeroSIdx.succ_injSIdx.succ_le_monoSIdx.succ_lt_monoSIdx.succ_neqSIdx.weak_case(ignored)SIdxFiniteSIdxMixinsidxChecklist
authorssection of any appropriate files