def AP.double_zero
import bend-osdev-array@0.1.0.1/PROOF.bend as PROOFimport Base
107def AP.double_zero(x: Nat, e: {Nat.double(x) == 0n : Nat}) -> {x == 0n : Nat}:
108 match x:
109 case 0n:
110 {==}
111 case 1n+p:
112 Empty.absurd({1n+p == 0n : Nat}, AP.sz(1n+Nat.double(p), e))