Theorem islan2

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

	Ref	Expression
Hypotheses	islan.r	$$⊢R=D\mathrm{FuncCat}E$$
	islan.s	$$⊢S=C\mathrm{FuncCat}E$$
	islan.k	No typesetting found for |- K = ( <. D , E >. -o.F F ) with typecode |-
Assertion	islan2	Could not format assertion : No typesetting found for |- ( L ( F ( <. C , D >. Lan E ) X ) A -> L ( K ( R UP S ) X ) A ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		islan.r	$$⊢R=D\mathrm{FuncCat}E$$
2		islan.s	$$⊢S=C\mathrm{FuncCat}E$$
3		islan.k	Could not format K = ( <. D , E >. -o.F F ) : No typesetting found for |- K = ( <. D , E >. -o.F F ) with typecode |-
4	1 2 3	islan	Could not format ( <. L , A >. e. ( F ( <. C , D >. Lan E ) X ) -> <. L , A >. e. ( K ( R UP S ) X ) ) : No typesetting found for |- ( <. L , A >. e. ( F ( <. C , D >. Lan E ) X ) -> <. L , A >. e. ( K ( R UP S ) X ) ) with typecode |-
5		df-br	Could not format ( L ( F ( <. C , D >. Lan E ) X ) A <-> <. L , A >. e. ( F ( <. C , D >. Lan E ) X ) ) : No typesetting found for |- ( L ( F ( <. C , D >. Lan E ) X ) A <-> <. L , A >. e. ( F ( <. C , D >. Lan E ) X ) ) with typecode |-
6		df-br	Could not format ( L ( K ( R UP S ) X ) A <-> <. L , A >. e. ( K ( R UP S ) X ) ) : No typesetting found for |- ( L ( K ( R UP S ) X ) A <-> <. L , A >. e. ( K ( R UP S ) X ) ) with typecode |-
7	4 5 6	3imtr4i	Could not format ( L ( F ( <. C , D >. Lan E ) X ) A -> L ( K ( R UP S ) X ) A ) : No typesetting found for |- ( L ( F ( <. C , D >. Lan E ) X ) A -> L ( K ( R UP S ) X ) A ) with typecode |-