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2項関係(19)

定理 shunting

R:{\mathop{\rm mapping}\nolimits}  \Rightarrow (P \circ R \subseteq Q \equiv P \subseteq Q \circ {R^T})
R:{\mathop{\rm mapping}\nolimits}  \Rightarrow ({R^T} \circ P \subseteq Q \equiv P \subseteq R \circ Q)
R:{\mathop{\rm bijective}\nolimits}  \Rightarrow (P \circ {R^T} \subseteq Q \equiv P \subseteq Q \circ R)
R:{\mathop{\rm bijective}\nolimits}  \Rightarrow (R \circ P \subseteq Q \equiv P \subseteq {R^T} \circ Q)

定理

P:{\mathop{\rm mapping}\nolimits}  \wedge Q:{\mathop{\rm mapping}\nolimits}  \Rightarrow (P \subseteq Q \circ R \equiv Q \subseteq P \circ {R^T})
P:{\mathop{\rm bijective}\nolimits}  \wedge Q:{\mathop{\rm bijective}\nolimits}  \Rightarrow (P \subseteq R \circ Q \equiv Q \subseteq {R^T} \circ P)

定理

R:{\mathop{\rm mapping}\nolimits}  \wedge S:{\mathop{\rm mapping}\nolimits}  \Rightarrow (R \subseteq S) = (R = S) = (S \subseteq R)
R:{\mathop{\rm bijective}\nolimits}  \wedge S:{\mathop{\rm bijective}\nolimits}  \Rightarrow (R \subseteq S) = (R = S) = (S \subseteq R)