How to automatically prove the simple equality of real numbers in Coq?

Question

What I'm looking for is a tactic autothat can prove simple equalities, such as:

1/2 = 2/4

So far, I have tried manually using ring_simplifyand field_simplifyto prove the equalities. Even this does not work well (Coq 8.5b3). The example below works:

Require Export Coq.Reals.RIneq.
Local Open Scope Z_scope.
Local Open Scope R_scope.

Example test2: 1 = 1 / 1.
Proof. field_simplify. field_simplify. reflexivity.
Qed. 

But had to be used field_simplfy twice before reflexivity. The first one field_simplfiygives me:

1 subgoal
______________________________________(1/1)
1 / 1 = 1 / 1 / (1 / 1)

which is not subject to reflexivity.

The example below does not work, field_simplifyit seems to do nothing with the goal, therefore, reflexivitycannot be used.

Example test3: 1/2 = 2/4.
Proof. field_simplify. reflexivity. 

Again, is there an automatic way to achieve this, for example field_auto?

Answer 1

, field - , .

Require Export Coq.Reals.RIneq.
Local Open Scope Z_scope.
Local Open Scope R_scope.


Example test3: 1/2 = 2/4.
Proof.  field. Qed.