Theorem isran2

Description: A right Kan extension is a universal pair. (Contributed by Zhi Wang, 4-Nov-2025)

	Ref	Expression
Hypotheses	isran.o	$$⊢O=\mathrm{oppCat}\left(D\mathrm{FuncCat}E\right)$$
	isran.p	$$⊢P=\mathrm{oppCat}\left(C\mathrm{FuncCat}E\right)$$
	isran.k	No typesetting found for |- ( ph -> ( <. D , E >. -o.F F ) = <. J , K >. ) with typecode |-
	isran2.l	No typesetting found for |- ( ph -> L ( F ( <. C , D >. Ran E ) X ) A ) with typecode |-
Assertion	isran2	Could not format assertion : No typesetting found for |- ( ph -> L ( <. J , tpos K >. ( O UP P ) X ) A ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		isran.o	$$⊢O=\mathrm{oppCat}\left(D\mathrm{FuncCat}E\right)$$
2		isran.p	$$⊢P=\mathrm{oppCat}\left(C\mathrm{FuncCat}E\right)$$
3		isran.k	Could not format ( ph -> ( <. D , E >. -o.F F ) = <. J , K >. ) : No typesetting found for |- ( ph -> ( <. D , E >. -o.F F ) = <. J , K >. ) with typecode |-
4		isran2.l	Could not format ( ph -> L ( F ( <. C , D >. Ran E ) X ) A ) : No typesetting found for |- ( ph -> L ( F ( <. C , D >. Ran E ) X ) A ) with typecode |-
5		df-br	Could not format ( L ( F ( <. C , D >. Ran E ) X ) A <-> <. L , A >. e. ( F ( <. C , D >. Ran E ) X ) ) : No typesetting found for |- ( L ( F ( <. C , D >. Ran E ) X ) A <-> <. L , A >. e. ( F ( <. C , D >. Ran E ) X ) ) with typecode |-
6	4 5	sylib	Could not format ( ph -> <. L , A >. e. ( F ( <. C , D >. Ran E ) X ) ) : No typesetting found for |- ( ph -> <. L , A >. e. ( F ( <. C , D >. Ran E ) X ) ) with typecode |-
7	1 2 3 6	isran	Could not format ( ph -> <. L , A >. e. ( <. J , tpos K >. ( O UP P ) X ) ) : No typesetting found for |- ( ph -> <. L , A >. e. ( <. J , tpos K >. ( O UP P ) X ) ) with typecode |-
8		df-br	Could not format ( L ( <. J , tpos K >. ( O UP P ) X ) A <-> <. L , A >. e. ( <. J , tpos K >. ( O UP P ) X ) ) : No typesetting found for |- ( L ( <. J , tpos K >. ( O UP P ) X ) A <-> <. L , A >. e. ( <. J , tpos K >. ( O UP P ) X ) ) with typecode |-
9	7 8	sylibr	Could not format ( ph -> L ( <. J , tpos K >. ( O UP P ) X ) A ) : No typesetting found for |- ( ph -> L ( <. J , tpos K >. ( O UP P ) X ) A ) with typecode |-