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Proof step 4 from proof getarray-in-01 (previous step)

¬ 1 < i1, 0 < i1, val ∈ getarray(r, i0, i1, st), ∀ 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ getarray(r, i, 1, st) = st[r -- i '] '
Proof step 3:
∀ st, i0, r, val, i. i→n(i) < i→n(1) → (val ∈ getarray(r, i0, i, st) ∧ 0 < i → (∃ i2. ¬ i2 < i0 ∧ ¬ i0 + i ≤ i2 ∧ st[r -- i2 '] = val)) ⊦ ∃ i. ¬ i < i0 ∧ ¬ i0 < i ∧ st[r -- i '] = st[r -- i0 ']

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ val ∈ val0 ' ↔ val = val0], [CSIMPSEQ : ⊦ 0 < i → (i ≤ 1 ↔ i = 1)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i])]]