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Proof step 13 from proof extension (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
st[r -- i '] .byteval = st0[r0 -- i0 '] .byteval, j < i2, 0 ≤ j, 0 < i2, ∀ j. ¬ i2 < j ∧ ¬ j < 0 → st[r -- (i + j) '] .byteval = st0[r0 -- (i0 + j) '] .byteval, ∀ st0, j0, i0, r0, st, i, r, j1. i→n(j1) < i→n(i2 + 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)) ⊦ bytevalues(getarray(r, i + 1, i2, st)) = bytevalues(getarray(r0, i0 + 1, i2, st0)), st[r -- ((i + 1) + j) '] .byteval = st0[r0 -- ((i0 + 1) + j) '] .byteval, 0 = i2

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])]]