Thm* 'a,'b:S. all( x:hsum('a; 'b). implies(isl(x),equal(inl(outl(x)),x))) | [hinl_houtl] |
Thm* 'c,'b,'a:S.
Thm* all
Thm* ( f:'a  'c. all
Thm* ( f:'a  'c. ( g:'b  'c. exists_unique
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. and
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. (all
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. (( x:'a. equal
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. (( x:'a. (h(inl(x))
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. (( x:'a. ,f(x)))
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. ,all
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. ,( x:'b. equal
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. ,( x:'b. (h(inr(x))
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. ,( x:'b. ,g(x))))))) | [hsum_axiom_2] |
Thm* 'c,'b,'a:S.
Thm* all
Thm* ( f:'a  'c. all
Thm* ( f:'a  'c. ( g:'b  'c. exists_unique
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. and
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. (equal(o(h,inl),f)
Thm* ( f:'a  'c. ( g:'b  'c. ( h:hsum('a; 'b)  'c. ,equal(o(h,inr),g))))) | [hsum_axiom] |
Thm* 'a,'b:S. all( x:'a. equal(outl(inl(x)),x)) | [houtl_wd] |
Thm* 'a,'b:S. and(all( x:'b. isr(inr(x))),all( y:'a. not(isr(inl(y))))) | [hisr_wd] |
Thm* 'b,'a:S. and(all( x:'a. isl(inl(x))),all( y:'b. not(isl(inr(y))))) | [hisl_wd] |
Thm* 'b,'a:S.
Thm* all
Thm* ( e:'a. equal(inl(e),abs_sum( b:hbool. x:'a. y:'b. and(equal(x,e),b)))) | [hinl_def] |