/usr/share/hol88-2.02.19940316/help/ENTRIES/GEN.doc is in hol88-help 2.02.19940316-35.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 37 38 39 40 | \DOC GEN
\TYPE {GEN : (term -> thm -> thm)}
\SYNOPSIS
Generalizes the conclusion of a theorem.
\KEYWORDS
rule, quantifier, universal.
\DESCRIBE
When applied to a term {x} and a theorem {A |- t}, the inference rule
{GEN} returns the theorem {A |- !x. t}, provided {x} is a variable not
free in any of the assumptions. There is no compulsion that {x} should
be free in {t}.
{
A |- t
------------ GEN "x" [where x is not free in A]
A |- !x. t
}
\FAILURE
Fails if {x} is not a variable, or if it is free in any of the assumptions.
\EXAMPLE
The following example shows how the above side-condition prevents
the derivation of the theorem {x=T |- !x. x=T}, which is clearly invalid.
{
#top_print print_all_thm;;
- : (thm -> void)
#let t = ASSUME "x=T";;
t = x = T |- x = T
#GEN "x:bool" t;;
evaluation failed GEN
}
\SEEALSO
GENL, GEN_ALL, GEN_TAC, SPEC, SPECL, SPEC_ALL, SPEC_TAC.
\ENDDOC
|