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Proof step 10 from proof arrayComp-02 (conclusion)

⊦ arraycomp(r1, i1, r2, i2, j, st) ∧ 0 ≤ j → (arraycomp(r1, i1, r2, i2, j + 1, st) ↔ st[r1 -- (i1 + j) '] = st[r2 -- (i2 + j) '])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ arraycomp(r1, i1, r2, i2, j, st) ↔ (∀ i. 0 ≤ i ∧ i < j → st[r1 -- (i1 + i) '] = st[r2 -- (i2 + i) '])
Proof step 9:
0 ≤ j, ∀ i. ¬ i < 0 ∧ ¬ j ≤ i → st[r1 -- (i1 + i) '] = st[r2 -- (i2 + i) '] ⊦ (∀ i. ¬ i < 0 ∧ ¬ j < i → st[r1 -- (i1 + i) '] = st[r2 -- (i2 + i) ']) ↔ st[r1 -- (i1 + j) '] = st[r2 -- (i2 + j) ']

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]