Add singleton word constructor to iset.mm #5142
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This is the syntax , df-s1 and some text in the section header. Copied without change from set.mm.
Stated as in set.mm. The proof is via fvprc , df-s1 and s1val
This is s1len from set.mm with a set existence condition added. The proof is similar to the set.mm proof.
The statement of the theorem and proof are taken from s1dmALT in set.mm. The comment is taken from s1dm in set.mm. Add s1dm and s1dmALT to mmil.html.
Stated as in set.mm. The proof is the set.mm proof with small changes.
Stated as in set.mm. The proof is the set.mm proof with small changes in various places.
Stated as in set.mm. The proof is the set.mm proof with small changes.
Stated as in set.mm. The proof is the set.mm proof with small changes.
This is ccatws1len from set.mm with a set existence condition on X . The proof is similar to the set.mm proof. Note that X does not need to be an element of V .
This is ccatws1lenp1b from set.mm with a set existence condition added. The proof is the set.mm proof with small changes.
This is ccats1val1 from set.mm with a set existence condition added. The proof is the set.mm proof with small changes.
Stated as in set.mm. The proof is the set.mm proof with small changes.
Stated as in set.mm. The proof is the set.mm proof with changes to various steps.
Stated as in set.mm. The proof is via ccatws1ls .
Stated as in set.mm. The proof is the set.mm proof with small changes.
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This is the section "Singleton words" and "Concatenations with singleton words".
Although we can prove theorems involving
<" X ">where X is a set, or where X is a proper class, set.mm uses excluded middle (directly or indirectly) to combine those cases. This is the biggest reason why these sections are intuitiionized incompletely or with changes.