Thm* as:(Label T) List, d:T, x:Label.
(x 1of(unzip(as)))  apply_alist(as;x;d) = d | [apply_alist_non_member] |
Thm* as:(Label T) List, d1,d2:T, x:Label.
(x 1of(unzip(as)))  apply_alist(as;x;d1) = apply_alist(as;x;d2) | [apply_alist_member2] |
Thm* as:(Label T) List, d:T, x:Label.
(x 1of(unzip(as)))  ( < x,apply_alist(as;x;d) > as) | [apply_alist_member] |
Thm* as:(Label T) List, p:(Label T), l:Label, d:T.
apply_alist([p / as];l;d) ~ if 1of(p) = l 2of(p) else apply_alist(as;l;d) fi | [apply_alist_cons] |
Thm* d:Top, l:Label. apply_alist(nil;l;d) ~ d | [apply_alist_nil] |
Thm* as:(Label T) List, d:T, x:Label.
(apply_alist(as;x;d) 2of(unzip(as))) apply_alist(as;x;d) = d | [apply_alist_property] |