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At:
inv pair functionality wrt one one corr113 1. A : Type
2. A' : Type
3. B : Type
4. B' : Type
5. f : AA' 6. g : A'A 7. x:A. g(f(x)) = x 8. y:A'. f(g(y)) = y 9. f' : BB' 10. g' : B'B 11. x:B. g'(f'(x)) = x 12. y:B'. f'(g'(y)) = y 13. (de.de/d,e. <f' o d o g,f o e o g'>) (AB)A'B' 14. (de.de/d,e. <g' o d o f,g o e o f'>) (A'B')AB f:((AB)A'B'), g:((A'B')AB). InvFuns(AB;A'B';f;g)
By:
Witness:
Wide.de/d,e. <f' o d o g,f o e o g'> |
Wide.de/d,e. <g' o d o f,g o e o f'>
THEN
Analyze THEN Analyze15 THEN New:[d | e] Analyze15
15. d : A'B' 16. e : B'A' 17. <d,e>/f,g. InvFuns(A';B';f;g)
(de.de/d,e. <f' o d o g,f o e o g'>)
((de.de/d,e. <g' o d o f,g o e o f'>)(<d,e>))
=
<d,e>
A'B'
2 steps
About:
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