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| | ===Fact 2.1=== | | ===Fact 2.1=== |
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| − | <pre>
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| − | Fact 2.1
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| − | If R c OxSxI,
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| − | then the following are identical subsets of SxI:
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| − | F2.1a. DerR :D13a
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| − | ::
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| − | F2.1b. Der(R) :D13b
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| − | ::
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| − | F2.1c. {<x, y> C SxI :
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| − | Den(R, x) = Den(R, y)
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| − | } :D13c
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| − | :R9a
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| − | ::
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| − | F2.1d. {<x, y> C SxI :
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| − | {Den(R, x)} = {Den(R, y)}
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| − | } :R9b
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| − | ::
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| − | F2.1e. {<x, y> C SxI :
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| − | for all o C O
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| − | {Den(R, x)}(o) = {Den(R, y)}(o)
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| − | } :R9c
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| − | ::
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| − | F2.1f. {<x, y> C SxI :
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| − | Conj(o C O)
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| − | {Den(R, x)}(o) = {Den(R, y)}(o)
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| − | } :R9d
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| − | ::
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| − | F2.1g. {<x, y> C SxI :
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| − | Conj(o C O)
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| − | (( {Den(R, x)}(o) , {Den(R, y)}(o) ))
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| − | } :R9e
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| − | ::
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| − | F2.1h. {<x, y> C SxI :
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| − | Conj(o C O)
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| − | (( {Den(R, x)} , {Den(R, y)} ))$(o)
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| − | } :R9f
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| − | :D12e
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| − | ::
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| − | F2.1i. {<x, y> C SxI :
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| − | Conj(o C O)
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| − | (( {ROS.x} , {ROS.y} ))$(o)
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| − | } :D12a
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| − | </pre>
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| − |
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| − | ====Variant 1====
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| − |
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| − | <br>
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| − |
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| − | {| 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%"
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| − | |
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| − | {| align="center" cellpadding="0" cellspacing="0" width="100%"
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| − | |- style="height:50px; text-align:center"
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| − | | style="width:80%" |
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| − | | style="width:20%; border-left:1px solid black" | <math>\operatorname{Fact~2.1}</math>
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| − | |}
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| − | |-
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| − | |
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| − | {| align="center" cellpadding="0" cellspacing="0" width="100%"
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| − | |- style="height:50px"
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| − | | width="2%" style="border-top:1px solid black" |
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| − | | width="10%" style="border-top:1px solid black" | <math>\text{If}\!</math>
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| − | | width="68%" style="border-top:1px solid black" | <math>L ~\subseteq~ O \times S \times I</math>
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| − | | width="20%" style="border-top:1px solid black; border-left:1px solid black" |
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| − | |- style="height:50px"
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| − | |
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| − | | <math>\text{then}\!</math>
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| − | | <math>\text{the following are identical subsets of}~ S \times I :</math>
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| − | | style="border-left:1px solid black" |
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| − | |}
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| − | |-
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| − | |
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| − | {| align="center" cellpadding="0" cellspacing="0" width="100%"
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| − | |- style="height:60px"
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| − | | width="2%" style="border-top:1px solid black" |
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| − | | width="10%" style="border-top:1px solid black" | <math>\operatorname{F2.1a.}</math>
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| − | | width="68%" style="border-top:1px solid black" | <math>\operatorname{Der}^L</math>
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| − | | width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{F2.1a~:~D13a}</math>
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| − | |- style="height:20px"
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| − | |
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| − | | style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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| − | |- style="height:40px"
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| − | |
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| − | | <math>\operatorname{F2.1b.}</math>
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| − | | <math>\operatorname{Der}(L)</math>
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| − | | style="border-left:1px solid black; text-align:center" |
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| − | <math>\operatorname{F2.1b~:~D13b}</math>
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| − | |- style="height:20px"
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| − | | style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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| − | |- style="height:60px"
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| − | |
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| − | | <math>\operatorname{F2.1c.}</math>
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| − | | <math>\{ (x, y) \in S \times I ~:~ \operatorname{Den}(L, x) ~=~ \operatorname{Den}(L, y) \}</math>
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| − | | style="border-left:1px solid black; text-align:center" |
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| − | <p><math>\operatorname{F2.1c~:~D13c}</math></p>
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| − | <p><math>\operatorname{F2.1c~:~R9a}</math></p>
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| − | |- style="height:20px"
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| − | |
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| − | | style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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| − | |- style="height:40px"
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| − | |
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| − | | <math>\operatorname{F2.1d.}</math>
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| − | | <math>\{ (x, y) \in S \times I ~:~ \upharpoonleft \operatorname{Den}(L, x) \upharpoonright ~=~ \upharpoonleft \operatorname{Den}(L, y) \upharpoonright \}</math>
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| − | | style="border-left:1px solid black; text-align:center" |
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| − | <math>\operatorname{F2.1d~:~R9b}</math>
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| − | |- style="height:20px"
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| − | |
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| − | | style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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| − | |- style="height:40px"
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| − | |
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| − | | <math>\operatorname{F2.1e.}</math>
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| − | | <math>\ldots</math>
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| − | | style="border-left:1px solid black; text-align:center" |
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| − | <math>\operatorname{F2.1e~:~R9c}</math>
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| − | |- style="height:20px"
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| − | | style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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| − | |- style="height:40px"
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| − | |
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| − | | <math>\operatorname{F2.1f.}</math>
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| − | | <math>\ldots</math>
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| − | | style="border-left:1px solid black; text-align:center" |
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| − | <math>\operatorname{F2.1f~:~R9d}</math>
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| − | |- style="height:20px"
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| − | | style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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| − | |- style="height:40px"
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| − | |
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| − | | <math>\operatorname{F2.1g.}</math>
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| − | | <math>\ldots</math>
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| − | | style="border-left:1px solid black; text-align:center" |
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| − | <math>\operatorname{F2.1g~:~R9e}</math>
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| − | |- style="height:20px"
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| − | |
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| − | | style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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| − | |- style="height:60px"
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| − | |
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| − | | <math>\operatorname{F2.1h.}</math>
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| − | | <math>\ldots</math>
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| − | | style="border-left:1px solid black; text-align:center" |
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| − | <p><math>\operatorname{F2.1h~:~R9f}</math></p>
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| − | <p><math>\operatorname{F2.1h~:~D12e}</math></p>
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| − | |- style="height:20px"
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| − | |
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| − | |
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| − | |
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| − | | style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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| − | |- style="height:40px"
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| − | |
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| − | | <math>\operatorname{F2.1i.}</math>
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| − | | <math>\ldots</math>
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| − | | style="border-left:1px solid black; text-align:center" |
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| − | <math>\operatorname{F2.1i~:~D12a}</math>
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| − | |}
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| − | |}
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| − |
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| − | <br>
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| − |
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| − | ====Variant 2====
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| | <br> | | <br> |
