Changes

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{| align="center" cellpadding="8" width="90%"

| <math>\upharpoonleft \operatorname{Der}(L) \upharpoonright (x, y) = \underset{o \in O}{\operatorname{Conj}} ~\underline{((}~ \upharpoonleft L_{SO} \upharpoonright (x, o) ~,~ \upharpoonleft L_{OS} \upharpoonright (o, y) ~\underline{))}~.</math>

| <math>\upharpoonleft \operatorname{Der}(L) \upharpoonright (x, y) \quad = \quad \underset{o \in O}{\operatorname{Conj}} ~\underline{((}~ \upharpoonleft L_{SO} \upharpoonright (x, o) ~,~ \upharpoonleft L_{OS} \upharpoonright (o, y) ~\underline{))}~.</math>

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| <math>\upharpoonleft P \circeq Q \upharpoonright (x, y) = \underset{m \in M}{\operatorname{Conj}} ~\underline{((}~ \upharpoonleft P \upharpoonright (x, m) ~,~ \upharpoonleft Q \upharpoonright (m, y) ~\underline{))}~.</math>

| <math>\upharpoonleft P \circeq Q \upharpoonright (x, y) \quad = \quad \underset{m \in M}{\operatorname{Conj}} ~\underline{((}~ \upharpoonleft P \upharpoonright (x, m) ~,~ \upharpoonleft Q \upharpoonright (m, y) ~\underline{))}~.</math>

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Compare this with the usual form of composition, typically notated <math>P \circ Q</math> and defined as follows:

Compare this with the usual form of composition, typically notated as "P.Q" and defined as follows:

{P.Q}(x, y) = Disj(m C M) ( {P}(x, m) . {Q}(m, y) ).

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</pre>

| <math>\upharpoonleft P \circ Q \upharpoonright (x, y) \quad = \quad \underset{m \in M}{\operatorname{Disj}} ~\upharpoonleft P \upharpoonright (x, m) ~\cdot~ \upharpoonleft Q \upharpoonright (m, y)~.</math>

==Appendices==

==Appendices==