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Proof step 22 from proof extension (previous step)

0 ≤ i1, ∀ 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 ' + bytevalues(getarray(r, i + 1, i1, st)) = bytevalues(getarray(r0, i0, j0, st0)) ↔ i1 + 1 = j0 ∧ (∀ j. j ≤ i1 ∧ 0 ≤ j → st[r -- (i + j) '] .byteval = st0[r0 -- (i0 + j) '] .byteval)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 < j → getarray(r, i, j, st) = st[r -- i '] ' + getarray(r, i + 1, j - 1, st)
Proof step 6:
⊦ j ≤ 0 → getarray(r, i, j, st) = []
Proof step 21:
0 < j0, 0 ≤ i1, ∀ 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 ' + bytevalues(getarray(r, i + 1, i1, st)) = bytevalues(st0[r0 -- i0 '] ' + getarray(r0, i0 + 1, j0 - 1, st0)) ↔ i1 + 1 = j0 ∧ (∀ j. j ≤ i1 ∧ 0 ≤ j → st[r -- (i + j) '] .byteval = st0[r0 -- (i0 + j) '] .byteval)

Rule argument

[crewrite-arg: get-rec-01, F, [st, j, i, r] → [st0, j0, i0, r0]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ bytevalues([]) = []], [CSIMPSEQ : ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = []], [CSIMPSEQ : ⊦ by ' ≠ []], [CSIMPSEQ : ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1], [CSIMPSEQ : ⊦ by ' + bytes ≠ []], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPFORWARD : ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1], [CSIMPFORWARD : ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0], [CSIMPSEQ : ⊦ i + j ≤ i ↔ j ≤ 0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (st0, j0, i0, r0)]]