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Proof step 3 from proof arrayComp-04 (conclusion)

⊦ arraycomp(r1, i1, r2, i2, j + j0, st) ∧ 0 < j ∧ 0 ≤ j0 → (st[r1 -- (i1 + j0) '] = st[r2 -- (i2 + j0) '] ↔ true)

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 2:
0 < j, 0 ≤ j0, ∀ i. ¬ i < 0 ∧ ¬ j + j0 ≤ i → st[r1 -- (i1 + i) '] = st[r2 -- (i2 + i) '] ⊦ st[r1 -- (i1 + j0) '] = st[r2 -- (i2 + j0) ']

Rule argument

[emptyarg]

Additional information

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