The axiom command recognises goals that are unconditionally valid, and marks them as being proven. As no sub-goals are generated, a pop-up message appears to confirm that the goal has been proven. It is rarely applied explicitly by the user, as cadiz automatically applies it whenever a sub-goal is generated to which it is applicable.
The goals that are regarded as axioms are ones that have a true consequent,
? true
or a false antecedent,
| false ?
or a consequent that is identical to an antecedent.
| p ? p
The command can be applied to the whole goal, or to any of the predicates that make the goal an axiom.
"axiom" g
This example applies the axiom command to goal g. The whole goal can always be referred to in a tactic as 0, which is useful when no joker bound to the goal is available.