Two axioms are in ADMIND[1,IGR].  The second one means that F(x)≤G(x), as 
a predicate of xεDom R1, admits induction weakly, if F(x) and G(x) are
continuous functions on Dom R1 into Dom R2.  Your axiom is a special case of this.
The first one characterizes AIW(P,R), and, hopefully, you can prove the second
one or any axiom of the same nature as a theorem relative to the first axiom
and you axiom system.  I would like to see you before I go any further.
I'll be at AI labo this weekend.	IGR

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07-JUL-72  1906		1,IGR