sn-wcdeq, 19.8aw #4251
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sn-wcdeq, 19.8aw #4251
+166
−149
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3rspcedvd replaced with 3rspcedvdw
avekens
reviewed
Sep 28, 2024
| df-resub $a |- -R = ( x e. RR , y e. RR |-> | ||
| ( iota_ z e. RR ( y + z ) = x ) ) $. | ||
| $} | ||
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| ${ | ||
| $d x y z A $. $d x y z B $. | ||
| $( Value of real subtraction, which is the (unique) real ` x ` such that | ||
| ` B + x = A ` . (Contributed by Steven Nguyen, 7-Jan-2022.) $) | ||
| ` B + x = A ` . (Contributed by Steven Nguyen, 7-Jan-2023.) $) | ||
| resubval $p |- ( ( A e. RR /\ B e. RR ) -> | ||
| ( A -R B ) = ( iota_ x e. RR ( B + x ) = A ) ) $= |
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The proof is still very long. Maybe some theorems/lemmas can be extracted.
avekens
approved these changes
Sep 28, 2024
benjub
reviewed
Sep 28, 2024
| @@ -646216,6 +646216,13 @@ D Fn ( I ... ( M - 1 ) ) /\ | |||
| ( cvv cv wnel cab wcel vex elirrv nelir 2th abbi2i eqcomi ) BACZMDZAENABMBF | |||
| NAGMMAHIJKL $. | |||
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| $( Alternative to ~ wcdeq and ~ df-cdeq . This flattens the syntax | |||
| representation ( wi ( weq vx vy ) wph ) to ( wcdeqALT vx vy wph ), | |||
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Suggested change
| representation ( wi ( weq vx vy ) wph ) to ( wcdeqALT vx vy wph ), | |
| representation ( wi ( weq vx vy ) wph ) to ( sn-wcdeq vx vy wph ), |
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| @@ -646216,6 +646216,13 @@ D Fn ( I ... ( M - 1 ) ) /\ | |||
| ( cvv cv wnel cab wcel vex elirrv nelir 2th abbi2i eqcomi ) BACZMDZAENABMBF | |||
| NAGMMAHIJKL $. | |||
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| $( Alternative to ~ wcdeq and ~ df-cdeq . This flattens the syntax | |||
| representation ( wi ( weq vx vy ) wph ) to ( wcdeqALT vx vy wph ), | |||
| accomplishing the stated purpose of ~ df-cleq . (Contributed by SN, | |||
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That does not really accomplish the purpose of df-cdeq (BTW, you wrote "df-cleq"). You could say it "illustrates the comment of df-cdeq". Overall, I find this theorem of dubious interest.
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It accomplishes what df-cdeq says it accomplishes: flattening the syntax tree
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Resolves #4158
The changes are rather disjoint but it's small (+146-147, +18, +2-2) and gets rid of 3 misc todos.