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Proof step 8 from proof getarray-union-03 (previous step)

r -- _length ∈ st ∧ 0 ≤ i + 1 ∧ j - 1 ≤ st[r -- _length] .intval - i + 1 ∧ (∀ i1. i + 1 ≤ i1 ∧ i1 < (i + 1) + (j - 1) → r -- i1 ' ∈ st) → getarray(r, i + 1, j - 1, st0 ∪ st) = getarray(r, i + 1, j - 1, st), 0 < j, 0 ≤ i, r ∈ st, j + i ≤ st[r -- _length] .intval, r -- _length ∈ st, r -- i ' ∈ st .keys, ∀ i0. ¬ i0 < i ∧ ¬ i + j ≤ i0 → r -- i0 ' ∈ st, ∀ st0, i, st, r, j0. i→n(j0) < i→n(j) → ( true → ( r -- _length ∈ st ∧ 0 ≤ i ∧ j0 ≤ st[r -- _length] .intval - i ∧ (∀ i1. i ≤ i1 ∧ i1 < i + j0 → r -- i1 ' ∈ st) → getarray(r, i, j0, st0 ∪ st) = getarray(r, i, j0, st))) ⊦ getarray(r, i + 1, j - 1, st0 ∪ st) = getarray(r, i + 1, j - 1, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
i < st[r -- _length] .intval, 1 < j + i, 0 < j + i, 0 < st[r -- _length] .intval, 0 < j, 0 ≤ i, r ∈ st, j + i ≤ st[r -- _length] .intval, r -- _length ∈ st, r -- i ' ∈ st .keys, i < i0, i0 < j + i, 0 < i0, i0 < st[r -- _length] .intval, 1 < st[r -- _length] .intval, ∀ i0. ¬ i0 < i ∧ ¬ i + j ≤ i0 → r -- i0 ' ∈ st, ∀ st0, i, st, r, j0. i→n(j0) < i→n(j) → ( true → ( r -- _length ∈ st ∧ 0 ≤ i ∧ j0 ≤ st[r -- _length] .intval - i ∧ (∀ i1. i ≤ i1 ∧ i1 < i + j0 → r -- i1 ' ∈ st) → getarray(r, i, j0, st0 ∪ st) = getarray(r, i, j0, st))) ⊦ getarray(r, i + 1, j - 1, st0 ∪ st) = getarray(r, i + 1, j - 1, st), r -- i0 ' ∈ st

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j], [CSIMPSEQ : ⊦ 0 < i → i1 < i1 + i], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ i < i0 ∧ i0 < i1 → i < i1], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPSEQ : ⊦ i + (j - i) = j], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j - i0 ↔ i + i0 ≤ j], [CSIMPSEQ : ⊦ i + j - i0 + j = i - i0], [CSIMPSEQ : ⊦ i + (j - i0) = i + j - i0], [CSIMPSEQ : ⊦ i - j ≤ i0 ↔ i ≤ j + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : i0 ≠ 0, i0 ≤ i ⊦ ((* i)) ≤ j → ((* i0)) ≤ j], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0])]]