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Proof step 23 from proof get-alleq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
0 < i1, ∀ j0, r, i, st, r0, i0, st0. i→n(j0) < i→n(i1 + 1) → (true → (getarray(r, i, j0, st) = getarray(r0, i0, j0, st0) ↔ (∀ j1. 0 ≤ j1 ∧ j1 < j0 → st[r -- (i + j1) '] = st0[r0 -- (i0 + j1) ']))) ⊦ getarray(r, i, i1, st) = getarray(r0, i0, i1, st0) ∧ st[r -- (i + i1) '] = st0[r0 -- (i0 + i1) '] ↔ (∀ j. j ≤ i1 ∧ 0 ≤ j → st[r -- (i + j) '] = st0[r0 -- (i0 + j) '])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ vals + val ' = vals0 + val0 ' ↔ vals = vals0 ∧ val = val0], [CSIMPSEQ : ⊦ vals + val = vals + val '], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ ((* i)) + i0 - ((* j)) = (i - j) + i0])]]