Move theorems to main and minimize ax-13 usage #3776
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* moved ~cbvrexvw, ~cbvrexw, ~cbvrexfw, ~cbvralvw, ~cbvralw, ~cbvralfw to main. * minimize with the new theorems.
GinoGiotto
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Jan 17, 2024
icecream17
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Jan 17, 2024
set.mm
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| ${ | ||
| $d x y A $. $d y ph $. $d x ps $. | ||
| cbvralvw.1 $e |- ( x = y -> ( ph <-> ps ) ) $. | ||
| $( Version of ~ cbvralv with a disjoint variable condition, which does not | ||
| require ~ ax-13 . (Contributed by Gino Giotto, 10-Jan-2024.) $) | ||
| cbvralvw $p |- ( A. x e. A ph <-> A. y e. A ps ) $= | ||
| ( nfv cbvralw ) ABCDEADGBCGFH $. | ||
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| $( Version of ~ cbvrexv with a disjoint variable condition, which does not | ||
| require ~ ax-13 . (Contributed by Gino Giotto, 10-Jan-2024.) $) | ||
| cbvrexvw $p |- ( E. x e. A ph <-> E. y e. A ps ) $= | ||
| ( nfv cbvrexw ) ABCDEADGBCGFH $. |
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for these two even more axioms can be saved by using cbvalvw and cbvexvw (non-blocking)
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Done (took me more time than I would like to admit to find the proofs).
tirix
approved these changes
Jan 18, 2024
avekens
approved these changes
Jan 18, 2024
icecream17
approved these changes
Jan 18, 2024
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Moved ~cbvrexvw, ~cbvrexw, ~cbvrexfw, ~cbvralvw, ~cbvralw, ~cbvralfw to main and use them to minimize ax-13 usage.
The following numbers are referring to the usage in the ax-13-complete branch:
Statement cbvralvw is used by 332 theorems.
Statement cbvrexvw is used by 273 theorems.
Statement cbvralw is used by 113 theorems.
Statement cbvrexw is used by 40 theorems.
Statement cbvralfw is used by 15 theorems.
Statement cbvrexfw is used by 18 theorems.
We cannot add disjoint variable conditions directly to the original versions unless we are down to add around 100 of them in a single PR (I counted an estimate to check if it was doable).
With this PR there are 64 theorems that drop ax-13 as a consequence: 241de13