"Well, I'm starting to run out of room on this whiteboard, so forgive me if I write that down in dath ilani shorthand," says Keltham.

    \ z. t1(z) -> ~t2(z)
    \ h. t3(h) -> t2(h)
__________________

    \ q. t1(q) -> ~t3(q)

"Now this is a valid reasoning rule to be sure," says Keltham, "but just like dividing over a balanced equation can be seen as multiplying by an inverse, I think we don't need to add this whole rule to our entity.  The form of this rule looks really quite similar, in some ways, to that earlier rule about Z-generalized, H-generalized, and Q-generalized.  I think we can add a smaller rule to our entity, which already has that rule, and get this rule back out as a special case - like adding the inverse operation to an algebra that already has the rule about multiplying over a balanced equation, and automatically getting out the power to divide over a balanced equation."

"I don't think, based on your past performance, that you can derive the missing rule on your own; but beliefs like that ought to be tested rather than just assumed.  Wanna surprise me?"

"Well, I'm starting to run out of room on this whiteboard, so forgive me if I write that down in dath ilani shorthand," says Keltham.

    \ z. t1(z) -> ~t2(z)
    \ h. t3(h) -> t2(h)
__________________

    \ q. t1(q) -> ~t3(q)

"Now this is a valid reasoning rule to be sure," says Keltham, "but just like dividing over a balanced equation can be seen as multiplying by an inverse, I think we don't need to add this whole rule to our entity.  The form of this rule looks really quite similar, in some ways, to that earlier rule about Z-generalized, H-generalized, and Q-generalized.  I think we can add a smaller new rule to our entity, which already has that previous rule, and get this rule back out as a special case - like adding the inverse operation to an algebra that already has the rule about multiplying over a balanced equation, and automatically getting out the power to divide over a balanced equation."

"I don't think, based on your past performance, that you can derive the missing rule on your own; but beliefs like that ought to be tested rather than just assumed.  Wanna surprise me?"

"Well, I'm starting to run out of room on this whiteboard, so forgive me if I write that down in dath ilani shorthand," says Keltham.

    \ z. t1(z) -> ~t2(z)
    \ h. t3(h) -> t2(h)
__________________

    \ q. t1(q) -> ~t3(q)

"Now this is a valid reasoning rule to be sure," says Keltham, "but just like dividing over a balanced equation can be seen as multiplying by an inverse, I think we don't need to add this whole rule to our entity.  The form of this rule looks really quite similar, in some ways, to that earlier rule about Z-generalized, H-generalized, and Q-generalized.  I think we can add a smaller new rule to our entity, which already has that previous rule, and get this rule back out as a special case - like adding the inverse operation to an algebra that already has the rule about multiplying over a balanced equation, and automatically getting out the power to divide over a balanced equation."

"I don't predict, based on your past performance, that you can derive the missing rule on your own; but beliefs like that ought to be tested rather than just assumed.  Wanna surprise me?"

"Well, I'm starting to run out of room on this wall, so forgive me if I write that down in dath ilani shorthand," says Keltham.

    \ z. t1(z) -> ~t2(z)
    \ h. t3(h) -> t2(h)
__________________

    \ q. t1(q) -> ~t3(q)

"Now this is a valid reasoning rule to be sure," says Keltham, "but just like dividing over a balanced equation can be seen as multiplying by an inverse, I think we don't need to add this whole rule to our entity.  The form of this rule looks really quite similar, in some ways, to that earlier rule about Z-generalized, H-generalized, and Q-generalized.  I think we can add a smaller new rule to our entity, which already has that previous rule, and get this rule back out as a special case - like adding the inverse operation to an algebra that already has the rule about multiplying over a balanced equation, and automatically getting out the power to divide over a balanced equation."

"I don't predict, based on your past performance, that you can derive the missing rule on your own; but beliefs like that ought to be tested rather than just assumed.  Wanna surprise me?"