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1. Alph: Type
2. L: LangOver(Alph)
3. EquivRel x,y:Alph*. x L-induced Equiv y
4. Fin(Alph)
5. Fin(x,y:Alph*//L-induced Equiv(x,y))
6. l:Alph*. Dec(L(l))
7. g: Alph*
8. t:Alph*. L(t) g(t)
9. a: Alph
10. s1: Alph*
11. s2: Alph*
12. z:Alph*. L(z @ s1) L(z @ s2)
13. z: Alph*
14. L((z @ [a]) @ s1) L((z @ [a]) @ s2)

L(z @ (a.s1)) L(z @ (a.s2))
By:
Unfold `languages` 2
THEN
RWH (LemmaC Thm* as,bs,cs:T*. ((as @ bs) @ cs) = (as @ (bs @ cs))) -1
Generated subgoal:

12. L: Alph*Prop
3. EquivRel x,y:Alph*. x L-induced Equiv y
4. Fin(Alph)
5. Fin(x,y:Alph*//L-induced Equiv(x,y))
6. l:Alph*. Dec(L(l))
7. g: Alph*
8. t:Alph*. L(t) g(t)
9. a: Alph
10. s1: Alph*
11. s2: Alph*
12. z:Alph*. L(z @ s1) L(z @ s2)
13. z: Alph*
14. L(z @ [a] @ s1) L(z @ [a] @ s2)
L(z @ (a.s1)) L(z @ (a.s2))

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