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Proof step 59 from proof range-copy-inner (previous step)

n + m0 ≤ # ar, (n3 + n1) + m0 ≤ # ar0, n3 + m0 ≤ m1 ⊦ range=(ar2, n2, copy(ar, n, ar0, n3 + n1, m0), n1, m1) ↔ range=(ar2, n2, ar0, n1, n3) ∧ range=(ar2, n3 + n2, ar, n, m0) ∧ range=(ar2, n3 + n2 + m0, ar0, (n3 + n1) + m0, m1 + n1 - m0 - n3 + n1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 58:
m1 + n1 - m0 = n0 + n3 + n1 ∧ n3 + n1 ≤ m1 + n1 - m0, n + m0 ≤ # ar, (n3 + n1) + m0 ≤ # ar0, n3 + m0 ≤ m1 ⊦ range=(ar2, n2, copy(ar, n, ar0, n3 + n1, m0), n1, m1) ↔ range=(ar2, n2, ar0, n1, n3) ∧ range=(ar2, n3 + n2, ar, n, m0) ∧ range=(ar2, n3 + n2 + m0, ar0, (n3 + n1) + m0, n0)

Rule argument

spec: nat inst: name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [m1 + n1 - m0, n3 + n1, n0] flags:

Additional information

[Concretesimprules((Csimpnamedseq(nat,,lels-01, ⊦ ¬ m ≤ n ↔ n < m) Csimpnamedseq(nat-basic2,,a, ⊦ (m + n0) + n1 = m + n0 + n1) Csimpnamedseq(nat-basic2,,c, ⊦ m + n = n + m) Csimpnamedseq(nat,,lels-04, ⊦ n + m ≤ m0 → ¬ n0 + m0 < m) Csimpnamedseq(nat,,ls-02, n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n) Csimpnamedseq(nat,,lep-02, ⊦ m + n ≤ m + n0 ↔ n ≤ n0) Csimpnamedseq(nat,,le-ls-simp, ⊦ m ≤ n → (n < m ↔ false)) Csimpelim(n ≤ m ⊦ n0 = m - n ↔ m = n0 + n))), Extraterms((m1 + n1 - m0n3 + n1n0))]