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Proof step 12 from proof getarray-in-01 (previous step)

i1 = i3 + 1, 1 < i1, 0 < i1, ∀ st, i0, r, val, i. i→n(i) < i→n(i1) → (val ∈ getarray(r, i0, i, st) ∧ 0 < i → (∃ i2. ¬ i2 < i0 ∧ ¬ i0 + i ≤ i2 ∧ st[r -- i2 '] = val)) ⊦ ∃ i. ¬ i < i0 ∧ ¬ i0 + i1 ≤ i ∧ st[r -- i '] = val, ¬ val ∈ getarray(r, i0, i3, st) ∧ val ≠ st[r -- (i0 + i1 - 1) ']

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
0 < i3, ∀ st, i0, r, val, i. i→n(i) < i→n(i3 + 1) → (val ∈ getarray(r, i0, i, st) ∧ 0 < i → (∃ i2. ¬ i2 < i0 ∧ ¬ i0 + i ≤ i2 ∧ st[r -- i2 '] = val)) ⊦ ∃ i. ¬ i < i0 ∧ ¬ i0 + i3 < i ∧ st[r -- i '] = val, ¬ val ∈ getarray(r, i0, i3, st) ∧ val ≠ st[r -- (i0 + i3) ']

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ ((* i)) + i0 - ((* j)) = (i - j) + i0], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ 0 < i ∧ 0 < j → 0 < i + j], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0])]]