Add sigma (df-sgm) to iset.mm #5049
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This is the sigma syntax and df-sgm . Copied without change from set.mm.
A natural number has finitely many divisors. The proof is taken from a portion of the phisum proof. Shorten the phisum proof using dvdsfi .
Stated as in set.mm. The proof is the set.mm proof with changes needed to use fsumcl instead of sumex .
Stated as in set.mm. The proof is the set.mm with a small change for differences in ^c theorems.
Stated as in set.mm. The proof is the set.mm proof with small changes related to differences in finite set theorems.
Stated as in set.mm. The proof is the set.mm proof with some small changes for differences in finiteness and ^c theorems.
Stated as in set.mm. The proof is the set.mm proof with small changes around theorems related to finiteness and nonempty sets.
This is cxpmul2 from set.mm but where the base has to be a positive real, not any complex number. The proof is based on a portion of the set.mm proof although most steps need some changes.
Deduction form of rpcxpmul2 .
Stated as in set.mm. The proof is the set.mm proof with some small changes related to set existence and differences in ^c theorems.
Stated as in set.mm. The proof is the set.mm with a few small changes to account for differences in finite set theorems.
Stated as in set.mm. The proof is the set.mm proof with a small change for differences in ^c theorems.
Stated as in set.mm. The proof is the set.mm proof with several changes for differences in ^c theorems and changing not equal to apart.
Stated as in set.mm. The proof is the set.mm proof with a few changes for set existence and apartness vs not equal.
Stated as in set.mm. The proof is the set.mm proof with changes for finite set theorems and set existence. In some parts of the proof the changes are significant but some parts of the proof, and the overall logic, are unchanged.
Stated as in set.mm. The proof is the set.mm with small changes for differences in ^c theorems.
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The definition and the theorems intuitionize without a lot of trouble.
Includes a few additions to
^ctheorems.Includes
dvdsfi(a natural number has finitely many divisors), extracted from a portion of thephisumproof.