Thm* 'a,'b:S, x:'a+'b. isr(x)  inr(outr(x)) = x | [inr_houtr] |
Thm* 'a,'b:S, x:'a+'b. isl(x)  inl(outl(x)) = x | [inl_houtl] |
Thm* 'c,'b,'a:S, f:('a 'c), g:('b 'c).
Thm* ( h:(('a+'b) 'c). ( x:'a. h(inl(x)) = f(x)) & ( x:'b. h(inr(x)) = g(x)))
Thm* & ( h,y:(('a+'b) 'c).
Thm* & (( x:'a. h(inl(x)) = f(x)) & ( x:'b. h(inr(x)) = g(x))
Thm* & (& ( x:'a. y(inl(x)) = f(x))
Thm* & (& ( x:'b. y(inr(x)) = g(x))
Thm* & (
Thm* & (h = y) | [sum_axiom_2] |
Thm* 'c,'b,'a:S, f:('a 'c), g:('b 'c).
Thm* ( h:(('a+'b) 'c).
Thm* (h o ( x:'a. inl(x)) = f 'a 'c & h o ( x:'b. inr(x)) = g 'b 'c)
Thm* & ( h,y:(('a+'b) 'c).
Thm* & (h o ( x:'a. inl(x)) = f 'a 'c & h o ( x:'b. inr(x)) = g 'b 'c
Thm* & (& y o ( x:'a. inl(x)) = f 'a 'c
Thm* & (& y o ( x:'b. inr(x)) = g 'b 'c
Thm* & (
Thm* & (h = y) | [sum_axiom] |
Thm* 'a,'b:S, u,v:'a+'b. rep_sum(u) = rep_sum(v)   'a 'b   u = v | [hrep_sum_inj] |
Thm* 'a,'b:S, u:'a+'b. isr(u)  outr(u) = outr(u) | [houtr_nuprl] |
Thm* 'a,'b:S, u:'a+'b. isl(u)  outl(u) = outl(u) | [houtl_nuprl] |