on 07-Oct-2020 (Wed)

Joining Rule: If x and y are theorems, then \(<x \land y>\) is a theorem

Separation Rule: If \(< x \land y >\) is a theorem, then both x and y are theorems.

Double-tilde Rule: The string '~~' can be deleted from any theorem. It can also be inserted into any theorem, provided that the resulting string is itself well-formed

Fantasy Rule: If y can be derived when x is assumed to be a theorem, then \(< x \supset y >\) is a theorem.

Carry-over Rule: Inside a fantasy, any theorem from the "reality" one level higher can be brought in and used

Rule of Detachment: If x and \(< x \supset y >\) are both theorems, then y is a theorem.

Contrapositive Rule: \(< x \supset y >\) and \(< \neg x \supset \neg y >\) are interchangeable.

De Morgans Rule: \(< \neg x \land \neg y>\) and \(\neg<x \lor y >\)are interchangeable

\(< \neg x \land \neg y>\) and \(\neg<x \lor y >\) are interchangeable

Switcheroo Rule: \(<x \lor y>\) and \(<\neg x \supset y>\) are interchangeable.