Language Proof and Logic 13.29

Any help with 10-12?

13.29 Remember that FOL assumes that claims are made about non-empty domains. You will need to use a name in giving this proof, even though no names appear in the original argument. Here is a nearly completed proof. You should fill in the details that are missing. 1. Yx (Small(x)> Cube(x)) 2. 3x -Cube(x) > ax Small(x) 3. Cube(c) v -Cube(c) Taut Con: 4. Cube(c) 5. 3x Cube(x) 6. Cube(c) 7. 3x-Cube(x) 8. 3x Small(x) aIntro: 4 3 Intro: 6 Elim: 7,2 9. dSmall(d) 10 ? Rule?: Rule?: Rule?: 12. 3x Cube(x) 13. ax Cube(x) ?3Elim: 9-12,8 14. 3x Cube(x) vElim: 4-5,6-13,3