Nuprl - Pf apply_alist_member 2 1 1

(12steps) PrintForm Definitions Lemmas mb automata 1 Sections GenAutomata Doc

At: apply alist member 2 1 1

1. T: Type
2. as: (LabelT) List
3. u: LabelT
4. v: (LabelT) List
5. d:T, x:Label. (x map(p.1of(p);v)) ( < x,apply_alist(v;x;d) > v)
6. d: T
7. x: Label
8. x = 1of(u) (x map(p.1of(p);v))
9. apply_alist([u / v];x;d) ~ if 1of(u) = x 2of(u) else apply_alist(v;x;d) fi

< x,if 1of(u) = x 2of(u) else apply_alist(v;x;d) fi > = u ( < x,if 1of(u) = x 2of(u) else apply_alist(v;x;d) fi > v)

By: SplitITE 0 THEN Try TrivialOr

Generated subgoals:

1 10. 1of(u) = x Pattern
< x,2of(u) > = u ( < x,2of(u) > v)

2 10. 1of(u) = x Pattern
< x,apply_alist(v;x;d) > = u ( < x,apply_alist(v;x;d) > v)

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(12steps) PrintForm Definitions Lemmas mb automata 1 Sections GenAutomata Doc