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Proof step 2 from proof numoc-swap (conclusion)

⊦ m < # ar ∧ n < # ar → #oc(a, ar[n, ar[m]][m, ar[n]], # ar) = #oc(a, ar, # ar)

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name:numoc-swap-gen seq: ⊦ m < # ar ∧ n < # ar ∧ n0 ≤ # ar → #oc(a, ar[n, ar[m]][m, ar[n]], n0) = (ar[m] = ar[n] ⊃ #oc(a, ar, n0) ;(m < n0 ⊃ (n < n0 ⊃ #oc(a, ar, n0) ;(a = ar[m] ⊃ #oc(a, ar, n0) - 1 ;(a = ar[n] ⊃ #oc(a, ar, n0) + 1 ;#oc(a, ar, n0) ) ) ) ;(n < n0 ⊃ (a = ar[n] ⊃ #oc(a, ar, n0) - 1 ;(a = ar[m] ⊃ #oc(a, ar, n0) + 1 ;#oc(a, ar, n0) ) ) ;#oc(a, ar, n0) ) ) ) subst:[m, ar, n, n0, a] → [m, ar, n, # ar, a] flags:current, []

Additional information

[Concretesimprules((Csimpnamedseq(nat,,ler, ⊦ m ≤ m))), Extraterms((marn# ara))]