If lj is not effectively ground there exists ν Ε rangefa). As μ
7
is an idem-
potent mgu, ν φ domainfaj) and ν Ε varsit). Thus, ν appears more than once
in {v^j :
V;
Ε vars(f)} and so ίμ· is restricted w.r.t. r.
LEMMA
11
Any inequation in a solvable system with an mgss is either effectively ground
or redundant.
Proof:
Let the system S consist of equation set Ε and inequations /
p
...,/
n
. Let
μ
Ε
be an idempotent mgu of Ε and let μ, be an idempotent mgu for Ε'
f
. = Ε
(
μ
Ε
.
Clearly soln(E''.) = soln(E U ...
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