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Add odZ to iset.mm #4261

Merged
merged 8 commits into from
Oct 3, 2024
Merged

Add odZ to iset.mm #4261

merged 8 commits into from
Oct 3, 2024

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jkingdon
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@jkingdon jkingdon commented Oct 2, 2024

This is the odZ syntax and all the theorems related to it in the section titled "Euler's theorem".

Everything here intuitionizes without a lot of trouble, although some parts of proofs need changes for decidability or theorems related to modulus and floor, but because we are dealing with integers or rational numbers, none of that is difficult.

Every theorem is stated as in set.mm.

This is the syntax odZ and the definition df-odz .  Copied without
change from set.mm.
Also, uniexd and supex2g .

Copied without change from set.mm.
This is a direct consequence of supex2g .

Add supex2g and infex2g to mmil.html.
Stated as in set.mm.  The proof is the set.mm proof with a small change
to use infex2g in place of infex .
Stated as in set.mm.

The proof of odzcl is as in set.mm.

The proof of odzcllem is similar to the set.mm proof but needs
intuitionizing around replacing infssuzcl with infssuzcldc .
Copied without change from set.mm.
Stated as in set.mm.  The proof needs no large change from the set.mm
proof, but many steps need intuitionizing for decidability or for
differences in floor and modulus theorems.
Copied without change from set.mm.
@jkingdon jkingdon merged commit 74f3a86 into metamath:develop Oct 3, 2024
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@jkingdon jkingdon deleted the odz branch October 3, 2024 14:46
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2 participants