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Proof step 18 from proof extension (previous step)

0 ≤ i1, 0 ≤ i2, ∀ st0, j0, i0, r0, st, i, r, j1. i→n(j1) < i→n(i1 + 1) → ( true → ( bytevalues(getarray(r, i, j1, st)) = bytevalues(getarray(r0, i0, j0, st0)) ↔ j1 = j0 ∧ (∀ j1. 0 ≤ j1 ∧ j1 < j0 → st[r -- (i + j1) '] .byteval = st0[r0 -- (i0 + j1) '] .byteval) ∧ ¬ j0 < 0 ∨ ¬ 0 < j1 ∧ ¬ 0 < j0)) ⊦ st[r -- i '] .byteval = st0[r0 -- i0 '] .byteval ∧ bytevalues(getarray(r, i + 1, i1, st)) = bytevalues(getarray(r0, i0 + 1, i2, st0)) ↔ (∀ j. j ≤ i2 ∧ 0 ≤ j → st[r -- (i + j) '] .byteval = st0[r0 -- (i0 + j) '] .byteval) ∧ i1 = i2

User applied rule apply induction

And obtained the following new goals

Proof step 17:
bytevalues(getarray(r, i + 1, i1, st)) = bytevalues(getarray(r0, i0 + 1, i2, st0)) ↔ i1 = i2 ∧ (∀ j1. 0 ≤ j1 ∧ j1 < i2 → st[r -- ((i + 1) + j1) '] .byteval = st0[r0 -- ((i0 + 1) + j1) '] .byteval) ∧ ¬ i2 < 0 ∨ ¬ 0 < i1 ∧ ¬ 0 < i2, 0 ≤ i1, 0 ≤ i2, ∀ st0, j0, i0, r0, st, i, r, j1. i→n(j1) < i→n(i1 + 1) → ( true → ( bytevalues(getarray(r, i, j1, st)) = bytevalues(getarray(r0, i0, j0, st0)) ↔ j1 = j0 ∧ (∀ j1. 0 ≤ j1 ∧ j1 < j0 → st[r -- (i + j1) '] .byteval = st0[r0 -- (i0 + j1) '] .byteval) ∧ ¬ j0 < 0 ∨ ¬ 0 < j1 ∧ ¬ 0 < j0)) ⊦ st[r -- i '] .byteval = st0[r0 -- i0 '] .byteval ∧ bytevalues(getarray(r, i + 1, i1, st)) = bytevalues(getarray(r0, i0 + 1, i2, st0)) ↔ (∀ j. j ≤ i2 ∧ 0 ≤ j → st[r -- (i + j) '] .byteval = st0[r0 -- (i0 + j) '] .byteval) ∧ i1 = i2

Rule argument

[substlist-arg: [st0, j0, i0, r0, st, i, r, j1] → [st0, i2, i0 + 1, r0, st, i + 1, r, i1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ 0 ≤ i → i→n(i + 1) = i→n(i) + 1], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j)], [CSIMPSEQ : ⊦ 0 ≤ i → abs(i) = i], [CSIMPSEQ : ⊦ ¬ i < i], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (st0, i2, i0 + 1, r0, st, i + 1, r, i1)]]