Last Update: 6 October 2010
Note: or material is highlighted |
Note: A username and password may be required to access certain documents. Please contact Bill Rapaport.
Index to all lecture notes
…Previous lecture
∀xA(x)
A(x := c) i.e., A(c)
where c could name any object in the domain
A(c)
∀xA(c := x) i.e.,
∀xA(x)
where c must name an arbitrary object in the
domain
not any particular or special one
(cf. proofs in geometry)
∃xA(x)
A(x := c) i.e., A(c)
where c must name an arbitrary object
in the domain,
not any particular one
i.e., c must be a brand-new name.
A(c)
∃xA(c := x) i.e.,
∃xA(x)
where c names some actual object in the domain that is known to satisfy A.
1 | ∀x[191(x) → Frosh(x)] | : | P1 |
2 | (191(fred) → Frosh(fred)) | : | 1; UI (x := fred) |
3 | 191(fred) | : | P3 |
4 | Frosh(fred) | : | 2,3: MP |
5 | ∀x[Frosh(x) → Pass(x)] | : | P2 |
6 | (Frosh(fred) → Pass(fred)) | : | 5; UI (x := fred) |
7 | Pass(fred) | : | 4,6; MP |
8 | (191(fred) ∧ Pass(fred)) | : | 3,7; Conj |
9 | ∃x[191(x) ∧ Pass(x)] | : | 8, EG (fred := x) |