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| ===Fact 2.2=== | | ===Fact 2.2=== |
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− | <pre>
| + | ====Variant 1==== |
− | Fact 2.2
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− | If R c OxSxI,
| + | <br> |
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− | then the following are equivalent: | + | {| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%" |
| + | | |
| + | {| align="center" cellpadding="0" cellspacing="0" width="100%" |
| + | |- style="height:50px; text-align:center" |
| + | | style="width:80%" | |
| + | | style="width:20%; border-left:1px solid black" | <math>\operatorname{Fact~2.2}</math> |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" cellpadding="0" cellspacing="0" width="100%" |
| + | |- style="height:50px" |
| + | | width="2%" style="border-top:1px solid black" | |
| + | | width="10%" style="border-top:1px solid black" | <math>\text{If}\!</math> |
| + | | width="68%" style="border-top:1px solid black" | <math>L ~\subseteq~ O \times S \times I</math> |
| + | | width="20%" style="border-top:1px solid black; border-left:1px solid black" | |
| + | |- style="height:50px" |
| + | | |
| + | | <math>\text{then}\!</math> |
| + | | <math>\text{the following are equivalent:}\!</math> |
| + | | style="border-left:1px solid black" | |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" cellpadding="0" cellspacing="0" style="text-align:center; width:100%" |
| + | |- style="height:60px" |
| + | | width="2%" style="border-top:1px solid black" | |
| + | | width="10%" style="border-top:1px solid black" | <math>\operatorname{F2.2a.}</math> |
| + | | width="16%" style="border-top:1px solid black" | <math>\operatorname{Der}^L</math> |
| + | | width="4%" style="border-top:1px solid black" | <math>=\!</math> |
| + | | width="48%" style="border-top:1px solid black" | <math>\ldots</math> |
| + | | width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{F2.2a~:~R11a}</math> |
| + | |- style="height:20px" |
| + | | colspan="5" | |
| + | | style="border-left:1px solid black; text-align:center" | <math>::\!</math> |
| + | |- style="height:40px" |
| + | | |
| + | | <math>\operatorname{F2.2b.}</math> |
| + | | <math>\upharpoonleft \operatorname{Der}^L \upharpoonright</math> |
| + | | <math>=\!</math> |
| + | | <math>\ldots</math> |
| + | | style="border-left:1px solid black; text-align:center" | |
| + | <math>\operatorname{F2.2b~:~R11b}</math> |
| + | |- style="height:20px" |
| + | | colspan="5" | |
| + | | style="border-left:1px solid black; text-align:center" | <math>::\!</math> |
| + | |- style="height:60px" |
| + | | |
| + | | <math>\operatorname{F2.2c.}</math> |
| + | | <math>\upharpoonleft \operatorname{Der}^L \upharpoonright</math> |
| + | | <math>=\!</math> |
| + | | <math>\ldots</math> |
| + | | style="border-left:1px solid black; text-align:center" | |
| + | <math>\operatorname{F2.2c~:~R11c}</math></p> |
| + | |- style="height:20px" |
| + | | colspan="5" | |
| + | | style="border-left:1px solid black; text-align:center" | <math>::\!</math> |
| + | |- style="height:60px" |
| + | | |
| + | | <math>\operatorname{F2.2d.}</math> |
| + | | <math>\upharpoonleft \operatorname{Der}^L \upharpoonright</math> |
| + | | <math>=\!</math> |
| + | | <math>\ldots</math> |
| + | | style="border-left:1px solid black; text-align:center" | |
| + | <math>\operatorname{F2.2d~:~Log}</math> |
| + | |- style="height:20px" |
| + | | colspan="5" | |
| + | | style="border-left:1px solid black; text-align:center" | <math>::\!</math> |
| + | |- style="height:60px" |
| + | | |
| + | | <math>\operatorname{F2.2e.}</math> |
| + | | <math>\upharpoonleft \operatorname{Der}^L \upharpoonright</math> |
| + | | <math>=\!</math> |
| + | | <math>\ldots</math> |
| + | | style="border-left:1px solid black; text-align:center" | |
| + | <math>\operatorname{F2.2e~:~Log}</math> |
| + | |- style="height:20px" |
| + | | colspan="5" | |
| + | | style="border-left:1px solid black; text-align:center" | <math>::\!</math> |
| + | |- style="height:60px" |
| + | | |
| + | | <math>\operatorname{F2.2f.}</math> |
| + | | <math>\upharpoonleft \operatorname{Der}^L \upharpoonright</math> |
| + | | <math>=\!</math> |
| + | | <math>\ldots</math> |
| + | | style="border-left:1px solid black; text-align:center" | |
| + | <math>\operatorname{F2.2f~:~$~}</math> |
| + | |} |
| + | |} |
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− | F2.2a. DerR = {<x, y> C SxI :
| + | <br> |
− | Conj(o C O)
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− | {Den(R, x)}(o) =
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− | {Den(R, y)}(o)
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− | } :R11a
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− | ::
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− | F2.2b. {DerR} = { {<x, y> C SxI :
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− | Conj(o C O)
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− | {Den(R, x)}(o) =
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− | {Den(R, y)}(o)
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− | }
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− | } :R11b
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− | ::
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− | F2.2c. {DerR} c SxIxB
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− | :
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− | {DerR} = {<x, y, v> C SxIxB :
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− | v =
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− | [ Conj(o C O)
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− | {Den(R, x)}(o) =
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− | {Den(R, y)}(o)
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− | ]
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− | } :R11c
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− | ::
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− | F2.2d. {DerR} = {<x, y, v> C SxIxB :
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− | v =
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− | Conj(o C O)
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− | [ {Den(R, x)}(o) =
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− | {Den(R, y)}(o)
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− | ]
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− | } :Log
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| | | |
− | F2.2e. {DerR} = {<x, y, v> C SxIxB :
| + | ====Variant 2==== |
− | v =
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− | Conj(o C O)
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− | (( {Den(R, x)}(o),
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− | {Den(R, y)}(o)
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− | ))
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− | } :Log
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− | | |
− | F2.2f. {DerR} = {<x, y, v> C SxIxB :
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− | v =
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− | Conj(o C O)
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− | (( {Den(R, x)},
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− | {Den(R, y)}
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− | ))$(o)
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− | } :$
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− | </pre>
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| <br> | | <br> |