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Proof step 3 from proof copy-atfield (previous step)

0 < j, ∀ j0, r1, i1, r2, i2, st, r, fs. i→n(j0) < i→n(j) → (true → (arraycopy(r1, i1, r2, i2, j0, st)[r -- fs ']) = st[r -- fs ']) ⊦ (arraycopy(r1, i1, r2, i2, j - 1, st[r2 -- (i2 + j - 1) ', st[r1 -- (i1 + j - 1) ']])[r -- fs ']) = st[r -- fs ']

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [j0, r1, i1, r2, i2, st, r, fs] → [j - 1, r1, i1, r2, i2, st[r2 -- (i2 + j - 1) ', st[r1 -- (i1 + j - 1) ']], r, fs] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i→n(i - 1) < i→n(i) ↔ 0 < i], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ fs ' ≠ i '])], [EXTRATERMS : (j - 1, r1, i1, r2, i2, st[r2 -- (i2 + j - 1) ', st[r1 -- (i1 + j - 1) ']], r, fs)]]