1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
|
\DOC FORALL_OR_CONV
\TYPE {FORALL_OR_CONV : conv}
\SYNOPSIS
Moves a universal quantification inwards through a disjunction.
\KEYWORDS
conversion, quantifier, universal, disjunction.
\DESCRIBE
When applied to a term of the form {!x. P \/ Q}, where {x} is not free in both
{P} and {Q}, {FORALL_OR_CONV} returns a theorem of one of three forms,
depending on occurrences of the variable {x} in {P} and {Q}. If {x} is free
in {P} but not in {Q}, then the theorem:
{
|- (!x. P \/ Q) = (!x.P) \/ Q
}
\noindent is returned. If {x} is free in {Q} but not in {P}, then the
result is:
{
|- (!x. P \/ Q) = P \/ (!x.Q)
}
\noindent And if {x} is free in neither {P} nor {Q}, then the result is:
{
|- (!x. P \/ Q) = (!x.P) \/ (!x.Q)
}
\FAILURE
{FORALL_OR_CONV} fails if it is applied to a term not of the form
{!x. P \/ Q}, or if it is applied to a term {!x. P \/ Q} in which the
variable {x} is free in both {P} and {Q}.
\SEEALSO
OR_FORALL_CONV, LEFT_OR_FORALL_CONV, RIGHT_OR_FORALL_CONV.
\ENDDOC
|
