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\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
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