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Proof step 28 from proof getbytearray-pseq-nojunk-02 (previous step)

st[r -- _type] .type = mkarraytype(byte_type), st[r -- _length] .intval = i2 + i, 0 ≤ i, 0 < i2 + i, ps=(r, st, r1, st1), i3 < i2, 0 < i2, 0 ≤ i2, 0 ≤ i3, ∀ i1, st1, r1, i0, r0, st0. i→n(st0[r0 -- _length] .intval - i0) < i→n(i2) → ( st0[r0 -- _type] .type = mkarraytype(byte_type) ∧ ps=(r0, st0, r1, st1) ∧ i0 < st0[r0 -- _length] .intval ∧ i0 + i1 ≤ st0[r0 -- _length] .intval ∧ 0 ≤ i0 ∧ 0 < st0[r0 -- _length] .intval ∧ 0 ≤ i1 → getbytearray(r0, i0, i1, st0) = getbytearray(r1, i0, i1, st1) ∨ r0 = jvmref ∨ junkref(`docs2store', r0, st0)) ⊦ getbytearray(r, i + 1, i3, st) = getbytearray(r1, i + 1, i3, st1), r = jvmref, junkref(`docs2store', r, st)

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [i1, st1, r1, i0, r0, st0] → [i3, st1, r1, i + 1, r, st] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j ≤ i ↔ j ≤ 0], [CSIMPSEQ : ⊦ 1 < i → abs(i) = i], [CSIMPSEQ : ⊦ i < j - i0 ↔ i + i0 < j], [CSIMPSEQ : ⊦ 1 ≤ i ↔ 0 < i], [CSIMPSEQ : ⊦ i ≤ j - i0 ↔ i + i0 ≤ j], [CSIMPSEQ : ⊦ 0 < i → abs(i - 1) = abs(i) - 1], [CSIMPSEQ : ⊦ i + j - i + 1 = j - 1], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 < i → 0 < j], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ 0 < j → abs(j) = j], [CSIMPSEQ : ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : i0 ≠ 0, i0 ≤ i ⊦ ((* i)) ≤ j → ((* i0)) ≤ j], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + j ≤ i0 + j ↔ i ≤ i0], [CSIMPSEQ : ⊦ 0 < i → (i ≤ 1 ↔ i = 1)], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPSEQ : ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPSEQ : ⊦ 0 ≤ i → (i < 1 ↔ i = 0)], [CSIMPSEQ : ⊦ getbytearray(r, i, 0, st) = []])], [EXTRATERMS : (i3, st1, r1, i + 1, r, st)]]