Thm* hyp,M,N:Formula List, q,r:Formula. |= < hyp,q.(M @ N) > |= < hyp,r.(M @ N) > |= < hyp,M @ (qr.N) > formula_and_right_sound

Thm* hyp,M,N:Formula List, q,r:Formula, a:Assignment. a | < hyp,q.(M @ N) > a | < hyp,r.(M @ N) > a | < hyp,M @ (qr.N) > formula_and_right_falsifiable

Thm* hyp,M,N:Formula List, q,r:Formula, a:Assignment. a |= < hyp,q.(M @ N) > & a |= < hyp,r.(M @ N) > a |= < hyp,M @ (qr.N) > formula_and_right_sat

Thm* concl,M,N:Formula List, q,r:Formula. |= < [q; r/ M @ N],concl > |= < M @ (qr.N),concl > formula_and_left_sound

Thm* concl,M,N:Formula List, q,r:Formula, a:Assignment. a | < [q; r/ M @ N],concl > a | < M @ (qr.N),concl > formula_and_left_falsifiable

Thm* concl,M,N:Formula List, q,r:Formula, a:Assignment. a |= < [q; r/ M @ N],concl > a |= < M @ (qr.N),concl > formula_and_left_sat

In prior sections: sat lemmas