Thm* all
Thm* ( P:hnum  hbool. implies
Thm* ( P:hnum  hbool. (and
Thm* ( P:hnum  hbool. ((P(0)
Thm* ( P:hnum  hbool. (,all
Thm* ( P:hnum  hbool. (,( n:hnum. implies
Thm* ( P:hnum  hbool. (,( n:hnum. (all( m:hnum. implies(lt(m,n),P(m)))
Thm* ( P:hnum  hbool. (,( n:hnum. ,P(n))))
Thm* ( P:hnum  hbool. ,all( n:hnum. P(n)))) | [hgen_induction] |
Thm* all
Thm* ( P:hnum  hbool. implies
Thm* ( P:hnum  hbool. (exists( n:hnum. P(n))
Thm* ( P:hnum  hbool. ,exists
Thm* ( P:hnum  hbool. ,( n:hnum. and
Thm* ( P:hnum  hbool. ,( n:hnum. (P(n)
Thm* ( P:hnum  hbool. ,( n:hnum. ,all( m:hnum. implies(lt(m,n),not(P(m)))))))) | [hwop] |
Thm* 'a:S.
Thm* all
Thm* ( f:'a  hbool. all
Thm* ( f:'a  hbool. ( x1:'a. all
Thm* ( f:'a  hbool. ( x1:'a. ( x2:'a. implies
Thm* ( f:'a  hbool. ( x1:'a. ( x2:'a. (and(f(x1),not(f(x2)))
Thm* ( f:'a  hbool. ( x1:'a. ( x2:'a. ,not(equal(x1,x2)))))) | [hfun_eq_lemma] |