Closed Jean-Luc-Picard-2021 closed 4 months ago
The Naoyuki Tamura seqprover for classical first-order logic invents a new variables, no Russell Paradox, which would read d(d):
------------------------------------------- Ax-c d(X1),d(Z) --> d(X1),d(Y1),X#(d(X)->Y@d(Y)) -------------------------------------------- R@ d(X1),d(Z) --> d(X1),Y@d(Y),X#(d(X)->Y@d(Y)) --------------------------------------------- R-> d(Z) --> d(X1),d(X1)->Y@d(Y),X#(d(X)->Y@d(Y)) --------------------------------------------- R#-c d(Z) --> d(X1),X#(d(X)->Y@d(Y)) -------------------------------- R@ d(Z) --> Y@d(Y),X#(d(X)->Y@d(Y)) ---------------------------------- R-> --> d(Z)->Y@d(Y),X#(d(X)->Y@d(Y)) ---------------------------------- R#-c --> X#(d(X)->Y@d(Y)) ------------------------ Ltop top --> X#(d(X)->Y@d(Y))
Was using Exy as a shorthand for set membership x e y. Was looking at this proof:
∃x(Exy → ∀zEzy) is valid. https://www.umsu.de/trees/#~7x%28Exy~5~6zEzy%29
In step 3 it shows Eyy. Could this not also be Eby? How does it choose y?