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Instead of proving (**forall** `x`: `G`) we assume
(~**forall** `x`: `G`), i.e.,
(**exists** `x`: ~`G`) and proceed to derive a contradiction:

~~>

Kforallx:G( ~~>

Kunion {existsx: ~G}F(alse) )

Kunion {~G[x<-a]}F(alse)

"We prove (**forall** `x`: `G`). Assume
~`G` for some `x`. Then ... (derivation of a contradiction
with additional knowledge ~`G`)."

*We will see later how to work with existential formulas in knowledge.*

Author: Wolfgang Schreiner

Last Modification: November 30, 1999