===== Submonoid =====
==== Meta ====
| @#55CCEE: context     | @#55CCEE: $\langle\!\langle M,*\rangle\!\rangle$ ... monoid |
| @#FFBB00: definiendum | @#FFBB00: $\langle\!\langle S,*\rangle\!\rangle\in$ it |
| @#AAFFAA: inclusion   | @#AAFFAA: $S\in$ closed monoid subset of $\langle\!\langle M,*\rangle\!\rangle$ |
| @#FFFDDD: exists      | @#FFFDDD: $e\in S$ |
| @#55EE55: postulate   | @#55EE55: $e$ ... unit of $\langle\!\langle M,*\rangle\!\rangle$ |

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=== Subset of ===
[[closed monoid subset]]