00100 GIVEAX(SCINDUCTION,(∀ R)(∀ F)(∀ P)(SCORDERING R ∧ FεDOMAIN(R→→R) 00200 ∧ Pε(DOMAIN R→TV) ∧AIW(P,R) ∧ β(P,UU)=T 00300 ∧ (∀ X)(XεDOMAIN R ∧ β(P,X)=T ⊃ β(P,β(F,X))=T) 00400 ⊃β(P,β(YCOMB(R),F))=T)); 00500 00600 GIVEAX(IGR1,(∀ R)(∀ P)(∀ Y)(SCORDERING R ∧ Pε(DOMAIN R → TV) 00700 ∧ (∀ X)(Xε DOMAIN R ⊃ (β(P,X)= T ≡ ββ(X,R,Y)=T)) 00800 ⊃ AIW(P,R))); 00500 END;