(5steps) PrintForm Definitions Lemmas mb automata 1 Sections GenAutomata Doc

At: apply alist member2 2

1. T: Type
2. as: (LabelT) List
3. u: LabelT
4. v: (LabelT) List
5. d1,d2:T, x:Label. (x 1of(unzip(v))) apply_alist(v;x;d1) = apply_alist(v;x;d2)

d1,d2:T, x:Label. (x 1of(unzip([u / v]))) apply_alist([u / v];x;d1) = apply_alist([u / v];x;d2)

By:
Auto
THEN
Inst Thm* as:(LabelT) List, p:(LabelT), l:Label, d:T. apply_alist([p / as];l;d) ~ if 1of(p) = l 2of(p) else apply_alist(as;l;d) fi [T;v;u;x;d1]
THEN
HypSubst -1 0
THEN
Thin -1
THEN
Inst Thm* as:(LabelT) List, p:(LabelT), l:Label, d:T. apply_alist([p / as];l;d) ~ if 1of(p) = l 2of(p) else apply_alist(as;l;d) fi [T;v;u;x;d2]
THEN
HypSubst -1 0
THEN
Thin -1
THEN
SplitOnConclITE


Generated subgoal:

16. d1: T
7. d2: T
8. x: Label
9. (x 1of(unzip([u / v])))
10. 1of(u) = x
apply_alist(v;x;d1) = apply_alist(v;x;d2)


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productlistconsuniverseequalimpliesall

(5steps) PrintForm Definitions Lemmas mb automata 1 Sections GenAutomata Doc