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Proof step 3 from proof range-extend (previous step)

range=(copy(ar, n, ar0, n0 + m0, m1), n0, ar1, n1, m0 + m1), n + m1 ≤ # ar, n0 + m0 + m1 ≤ # ar0 ⊦ range=(ar0, n0, ar1, n1, m0) ∧ range=(ar, n, ar1, n1 + m0, m1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ range=(ar0, n0, ar1, n1, m0 + m1) ↔ range=(ar0, n0, ar1, n1, m0) ∧ range=(ar0, n0 + m0, ar1, n1 + m0, m1)
Proof step 5:
range=(copy(ar, n, ar0, n0 + m0, m1), n0, ar1, n1, m0), range=(copy(ar, n, ar0, n0 + m0, m1), n0 + m0, ar1, n1 + m0, m1), n0 + m0 + m1 ≤ # ar0, n + m1 ≤ # ar ⊦ range=(ar0, n0, ar1, n1, m0) ∧ range=(ar, n, ar1, n1 + m0, m1)

Rule argument

spec: <toplevel> name: range-eq-append seq: ⊦ range=(ar0, n0, ar1, n1, m0 + m1) ↔ range=(ar0, n0, ar1, n1, m0) ∧ range=(ar0, n0 + m0, ar1, n1 + m0, m1) subst: [m1, m0, n1, ar1, n0, ar0] → [m1, m0, n1, ar1, n0, copy(ar, n, ar0, n0 + m0, m1)] flags: <all paths>

Additional information

Used terms: m1, m0, n1, ar1, n0, copy(ar, n, ar0, n0 + m0, m1)