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Proof step 5 from proof arrayComp-01 (previous step)

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) ']

User applied rule case distinction

And obtained the following new goals

Proof step 2:
∀ i. ¬ i < 0 ∧ ¬ j < i → st[r1 -- (i1 + i) '] = st[r2 -- (i2 + i) '], 0 < j, ∀ i. ¬ i < 0 ∧ ¬ j ≤ i → st[r1 -- (i1 + i) '] = st[r2 -- (i2 + i) '] ⊦ st[r1 -- (i1 + j) '] = st[r2 -- (i2 + j) ']
Proof step 4:
st[r1 -- (i1 + j) '] = st[r2 -- (i2 + j) '], 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) ']

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]