āØāØ āāg. ā¬*[ā», šā“iāµ] L ā” ā & šā¦gā¦ & f = ā*[i] ā«Æg
| āāg,I,K,V. K ā¢ š
*ā¦Vā¦ ā” g &
ā¬*[i] L ā” K.ā{I}V & f = ā*[i] ā«Æg
- | āāg,I,K. ā¬*[i] L ā” K.ā¤{I} & f = ā*[i] ā«Æg.
+ | āāg,I,K. ā¬*[i] L ā” K.ā¤{I} & šā¦gā¦ & f = ā*[i] ā«Æg.
#L elim L -L
[ #i #g | #L #I #IH * [ #g cases I -I [ #I | #I #V ] -IH | #i #g ] ] #H
[ elim (frees_inv_atom ā¦ H) -H #f #Hf #H destruct
/3 width=3 by or3_intro0, ex3_intro/
| elim (frees_inv_unit ā¦ H) -H #f #Hf #H destruct
- /4 width=3 by drops_refl, or3_intro2, ex2_3_intro/
+ /4 width=3 by drops_refl, or3_intro2, ex3_3_intro/
| elim (frees_inv_pair ā¦ H) -H #f #Hf #H destruct
/4 width=7 by drops_refl, or3_intro1, ex3_4_intro/
| elim (frees_inv_lref ā¦ H) -H #f #Hf #H destruct
elim (IH ā¦ Hf) -IH -Hf *
[ /4 width=3 by drops_drop, or3_intro0, ex3_intro/
| /4 width=7 by drops_drop, or3_intro1, ex3_4_intro/
- | /4 width=3 by drops_drop, or3_intro2, ex2_3_intro/
+ | /4 width=3 by drops_drop, or3_intro2, ex3_3_intro/
]
]
qed-.