Commit eb563833 authored by Robbert Krebbers's avatar Robbert Krebbers

Revert "prelude: add notation for > and >= for all kinds of numbers"

This reverts commit 24fa20e5.

Although these symmetric variants sometimes look "better", they
are really annoying and should IMHO never be used:

1.) For lemmas there is now a choice between >= and <=. Since there is
no longer a canonical choice, it is very easy to introduce a lot of
inconsistencies in statements of lemmas.

2.) For automation the situation becomes annoying, you have to built in
stuff for both >= and <=. That is very error-prone.

3.) For N and Z the notions x <= y and y >= x are not even convertible!
That means that done/by does not solve x <= y if you have y >= x and if
avoids you applying certain lemmas.
parent fdec4152
......@@ -28,10 +28,6 @@ Notation "x ≤ y ≤ z ≤ z'" := (x ≤ y ∧ y ≤ z ∧ z ≤ z')%nat : nat_
Notation "(≤)" := le (only parsing) : nat_scope.
Notation "(<)" := lt (only parsing) : nat_scope.
Infix "≥" := ge : nat_scope.
Notation "(≥)" := ge (only parsing) : nat_scope.
Notation "(>)" := gt (only parsing) : nat_scope.
Infix "`div`" := Nat.div (at level 35) : nat_scope.
Infix "`mod`" := Nat.modulo (at level 35) : nat_scope.
......@@ -108,10 +104,6 @@ Notation "(<)" := Pos.lt (only parsing) : positive_scope.
Notation "(~0)" := xO (only parsing) : positive_scope.
Notation "(~1)" := xI (only parsing) : positive_scope.
Infix "≥" := Pos.ge : positive_scope.
Notation "(≥)" := Pos.ge (only parsing) : positive_scope.
Notation "(>)" := Pos.gt (only parsing) : positive_scope.
Arguments Pos.of_nat _ : simpl never.
Instance positive_eq_dec: x y : positive, Decision (x = y) := Pos.eq_dec.
Instance positive_inhabited: Inhabited positive := populate 1.
......@@ -187,11 +179,6 @@ Notation "x < y ≤ z" := (x < y ∧ y ≤ z)%N : N_scope.
Notation "x ≤ y ≤ z ≤ z'" := (x y y z z z')%N : N_scope.
Notation "(≤)" := N.le (only parsing) : N_scope.
Notation "(<)" := N.lt (only parsing) : N_scope.
Infix "≥" := N.ge : N_scope.
Notation "(≥)" := N.ge (only parsing) : N_scope.
Notation "(>)" := N.gt (only parsing) : N_scope.
Infix "`div`" := N.div (at level 35) : N_scope.
Infix "`mod`" := N.modulo (at level 35) : N_scope.
......@@ -226,10 +213,6 @@ Notation "x ≤ y ≤ z ≤ z'" := (x ≤ y ∧ y ≤ z ∧ z ≤ z') : Z_scope.
Notation "(≤)" := Z.le (only parsing) : Z_scope.
Notation "(<)" := Z.lt (only parsing) : Z_scope.
Infix "≥" := Z.ge : Z_scope.
Notation "(≥)" := Z.ge (only parsing) : Z_scope.
Notation "(>)" := Z.gt (only parsing) : Z_scope.
Infix "`div`" := Z.div (at level 35) : Z_scope.
Infix "`mod`" := Z.modulo (at level 35) : Z_scope.
Infix "`quot`" := Z.quot (at level 35) : Z_scope.
......@@ -345,10 +328,6 @@ Notation "x ≤ y ≤ z ≤ z'" := (x ≤ y ∧ y ≤ z ∧ z ≤ z') : Qc_scope
Notation "(≤)" := Qcle (only parsing) : Qc_scope.
Notation "(<)" := Qclt (only parsing) : Qc_scope.
Infix "≥" := Qcge : Qc_scope.
Notation "(≥)" := Qcge (only parsing) : Qc_scope.
Notation "(>)" := Qcgt (only parsing) : Qc_scope.
Hint Extern 1 (_ _) => reflexivity || discriminate.
Arguments Qred _ : simpl never.
......
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