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Proof step 33 from proof copy-succ (previous step)

0 ≤ j ⊦ r = r0, ((rk = r0 -- (i0 + j) ' ⊃ st[r -- (i + j) ']; arraycopy(r, i, r0, i0, j, st)[rk])) = (arraycopy(r, i, r0, i0, j, st[r0 -- (i0 + j) ', st[r -- (i + j) ']])[rk]) ∧ ( rk ∈ (arraycopy(r, i, r0, i0, j, st)[r0 -- (i0 + j) ', st[r -- (i + j) ']]) ↔ rk ∈ arraycopy(r, i, r0, i0, j, st[r0 -- (i0 + j) ', st[r -- (i + j) ']]))

User applied rule structural induction

And obtained the following new goals

Proof step 32:
⊦ 0 ≤ j → r1 = r0 ∨ ((r -- sk = r0 -- (i0 + j) ' ⊃ st[r1 -- (i + j) ']; arraycopy(r1, i, r0, i0, j, st)[r -- sk])) = (arraycopy(r1, i, r0, i0, j, st[r0 -- (i0 + j) ', st[r1 -- (i + j) ']])[r -- sk]) ∧ ( r -- sk ∈ (arraycopy(r1, i, r0, i0, j, st)[r0 -- (i0 + j) ', st[r1 -- (i + j) ']]) ↔ r -- sk ∈ arraycopy(r1, i, r0, i0, j, st[r0 -- (i0 + j) ', st[r1 -- (i + j) ']]))

Rule argument

[VARWITHFMAVARSARG : rk, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : refkey generated by --;])]]