Matching. from the right to the correct
location in the proof box. universe of discourse = the counting numbers: 1,2,3, etc. Now, show that the sentence (1) '(%w)(^z)Gzw'
is |

Assume
__________

Then _________

But
________

So, _________

But ________

(for
contradiction) that

'(%w)(^z)Gzw' is*true*.

'(%w)(^z)Gzw' is

(^z)Gzn

must also be true (where 'n' is picked to name the appropriate number).

because
'(^z)Gzn' is true, *all* it's substitution
instances must be true.

'(^z)Gzn's substitution instance

Gnn

is true.

Gnn

is true.

this last result that 'Gnn' is is true is an absurdity for no number is greater than itself!

Hence, the initial assumption is wrong and (*) is false.

Q.E.D. |