Coq.Reals.DiscrR

# Module Coq.Reals.DiscrR

``Require` Rbase.

`Recursive` `Tactic` `Definition` Isrealint trm:=
`Match` trm With
| [``0``] -> Idtac
| [``1``] -> Idtac
| [``?1+?2``] -> (Isrealint ?1);(Isrealint ?2)
| [``?1-?2``] -> (Isrealint ?1);(Isrealint ?2)
| [``?1*?2``] -> (Isrealint ?1);(Isrealint ?2)
| [``-?1``] -> (Isrealint ?1)
| _ -> Fail.

`Recursive` `Tactic` `Definition` Sup0 :=
`Match` Context With
| [ |- ``1>0`` ] -> Unfold Rgt;Apply Rlt_R0_R1
| [ |- ``1+?1>0`` ] ->
Apply (Rgt_trans ``1+?1`` ?1 ``0``);
[Pattern 1 ``1+?1``;Rewrite Rplus_sym;Unfold Rgt;
Apply Rlt_r_r_plus_R1|Sup0].

`Tactic` `Definition` DiscrR :=
Try `Match` Context With
| [ |- ~(?1==?2) ] ->
Isrealint ?1;Isrealint ?2;
Apply Rminus_not_eq; Ring ``?1-?2``;
(`Match` Context With
| [ |- [``-1``] ] ->
Repeat Rewrite <- Ropp_distr1;Apply Ropp_neq
| _ -> Idtac);Apply Rgt_not_eq;Sup0.

`

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