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
|
\DOC LE_IMP
\TYPE {LE_IMP : thm -> thm}
\SYNOPSIS
Perform transitivity chaining for non-strict natural number inequality.
\DESCRIBE
When applied to a theorem {A |- s <= t} where {s} and {t} have type {num}, the
rule {LE_IMP} returns {A |- !x1...xn z. t <= z ==> s <= z}, where {z} is some
variable and the {x1,...,xn} are free variables in {s} and {t}.
\FAILURE
Fails if applied to a theorem whose conclusion is not of the form {`s <= t`}
for some natural number terms {s} and {t}.
\EXAMPLE
{
# LE_IMP (ARITH_RULE `n <= SUC(m + n)`);;
val it : thm = |- !m n p. SUC (m + n) <= p ==> n <= p
}
\USES
Can make transitivity chaining in goals easier, e.g. by
{FIRST_ASSUM(MATCH_MP_TAC o LE_IMP)}.
\SEEALSO
ARITH_RULE, REAL_LE_IMP, REAL_LET_IMP.
\ENDDOC
|
