/usr/share/axiom-20170501/src/algebra/CABMON.spad is in axiom-source 20170501-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | )abbrev category CABMON CancellationAbelianMonoid
++ Description:
++ This is an \spadtype{AbelianMonoid} with the cancellation property, \br
++ \tab{5}\spad{ a+b = a+c => b=c }.\br
++ This is formalised by the partial subtraction operator,
++ which satisfies the Axioms\br
++ \tab{5}\spad{c = a+b <=> c-b = a}
CancellationAbelianMonoid() : Category == SIG where
SIG ==> AbelianMonoid with
subtractIfCan : (%,%) -> Union(%,"failed")
++ subtractIfCan(x, y) returns an element z such that \spad{z+y=x}
++ or "failed" if no such element exists.
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