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Proof step 6 from proof arrayComp-02 (previous step)

0 ≤ j, ¬ j -1 < 0 ∧ ¬ j ≤ j -1 → st[r1 -- (i1 + j -1) '] = st[r2 -- (i2 + j -1) '], ∀ 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) ']

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 ≤ j, ∀ i. ¬ i < 0 ∧ ¬ j ≤ i → st[r1 -- (i1 + i) '] = st[r2 -- (i2 + i) '], j ≠ 0 → st[r1 -- (i1 + j - 1) '] = st[r2 -- (i2 + j - 1) '] ⊦ (∀ 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 : ([CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i + (j - i0) = i + j - i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j ≤ i ↔ j ≤ 0], [CSIMPSEQ : ⊦ i ≤ j - i0 ↔ i + i0 ≤ j], [CSIMPSEQ : ⊦ 0 ≤ i → (i < 1 ↔ i = 0)], [CSIMPSEQ : ⊦ i - j < i0 ↔ i < j + i0], [CSIMPSEQ : ⊦ i -1 = i - 1])]]