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Proof step 1 from proof violations-swap (conclusion)
n + 1 < # x ⊦ x[n + 1] < x[n] → violations(x[n, x[n + 1]][n + 1, x[n]]) = violations(x) - 1
System applied rule normalize
And obtained the following new goals
Proof step 2
:
x[n + 1] < x[n], n + 1 < # x ⊦ violations(x[n, x[n + 1]][n + 1, x[n]]) = violations(x) - 1
Rule argument
Additional information