[Imprint][Data Privacy Statement][E-Mail]

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Proof step 10 from proof copy-same-01-01 (previous step)

r2 ∈ st0, 0 < i3, 0 ≤ i, 0 ≤ i2, exactarray(r2, int_type, st0), i < i3, i2 + i3 ≤ st0[r2 -- _length] .intval ⊦ r2 = jvmref, r1 = r2, (r2 -- i0 ' ∈ arraycopy(r1, i1, r2, i2, i3, st0[r2 -- (i2 + i) ', val]) ↔ r2 -- i0 ' ∈ arraycopy(r1, i1, r2, i2, i3, st0)) ∧ (arraycopy(r1, i1, r2, i2, i3, st0[r2 -- (i2 + i) ', val])[r2 -- i0 ']) = (arraycopy(r1, i1, r2, i2, i3, st0)[r2 -- i0 ']), ¬ i0 < i2 ∧ ¬ i2 + i3 ≤ i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ j0 < i0 → (arraycopy(r, i, r0, i0, j, st)[r0 -- j0 ']) = st[r0 -- j0 ']
Proof step 7:
¬ i0 < i2, r2 ∈ st0, 0 < i3, 0 ≤ i, 0 ≤ i2, exactarray(r2, int_type, st0), i < i3, i2 + i3 ≤ st0[r2 -- _length] .intval ⊦ r2 = jvmref, r1 = r2, (r2 -- i0 ' ∈ arraycopy(r1, i1, r2, i2, i3, st0[r2 -- (i2 + i) ', val]) ↔ r2 -- i0 ' ∈ arraycopy(r1, i1, r2, i2, i3, st0)) ∧ (arraycopy(r1, i1, r2, i2, i3, st0[r2 -- (i2 + i) ', val])[r2 -- i0 ']) = (arraycopy(r1, i1, r2, i2, i3, st0)[r2 -- i0 ']), ¬ i0 < i2 ∧ ¬ i2 + i3 ≤ i0
Proof step 9:
i0 < i2, r2 ∈ st0, 0 < i3, 0 ≤ i, 0 ≤ i2, exactarray(r2, int_type, st0), i < i3, i2 + i3 ≤ st0[r2 -- _length] .intval ⊦ r2 = jvmref, r1 = r2, (r2 -- i0 ' ∈ arraycopy(r1, i1, r2, i2, i3, st0[r2 -- (i2 + i) ', val]) ↔ r2 -- i0 ' ∈ arraycopy(r1, i1, r2, i2, i3, st0)) ∧ (st0[r2 -- (i2 + i) ', val][r2 -- i0 ']) = (arraycopy(r1, i1, r2, i2, i3, st0)[r2 -- i0 ']), ¬ i0 < i2 ∧ ¬ i2 + i3 ≤ i0

Rule argument

[speclemmaarg: , j0 < i0 → (arraycopy(r, i, r0, i0, j, st)[r0 -- j0 ']) = st[r0 -- j0 '] ,[j0, st, j, i0, r0, i, r] → [i0, st0[r2 -- (i2 + i) ', val], i3, i2, r2, i1, r1] ,F ,storearrays , ,copy-lower ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i0, st0[r2 -- (i2 + i) ', val], i3, i2, r2, i1, r1)]]