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Proof step 33 from proof isarray-put-array-badindex (previous step)

r0 -- j ' ≠ r -- i ', st[r0 -- _type] = typeval(mkarraytype(ty)), st[r0 -- _length] = intval(i0), 0 < i0, 0 ≤ j, r0 -- _length ∈ st, 0 ≤ i0, i < 0, r0 -- _type ∈ st, r0 ∈ st, j < i0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r0 -- j '], ty), ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → r0 -- j0 ' ∈ st ⊦ r0 = jvmref, okval(st[r0 -- j '], ty)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
st[r0 -- _type] = typeval(mkarraytype(ty)), st[r0 -- _length] = intval(i0), 0 < i0, 0 ≤ j, r0 -- _length ∈ st, 0 ≤ i0, i < 0, r0 -- _type ∈ st, r0 ∈ st, j < i0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r0 -- j '], ty), ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → r0 -- j0 ' ∈ st ⊦ r0 = jvmref, j = i, okval(st[r0 -- j '], ty)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : int-abs, , lels-04, ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPNAMEDSEQ : int-abs, , zero-gels-01, ⊦ i < 0 ∧ 0 ≤ j → i < j], [CSIMPNAMEDSEQ : storekey, , inj-04, ⊦ i ' = i0 ' ↔ i = i0], [CSIMPNAMEDSEQ : refkey, , inj-01, ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]