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Proof step 34 from proof isarray-put-array-badindex (previous step)

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[r -- i ', val][r0 -- j '], ty)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]
Proof step 33:
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)

Rule argument

[x0lemmaarg: spec-name: store instance-name: javastore lemma-name: At-other antecedent: succedent: rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] substlist: [rk, val, rk0, st] → [r0 -- j ', val, r -- i ', st] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 1, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : refkey, , inj, ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPNAMEDSEQ : storekey, , inj-04, ⊦ i ' = i0 ' ↔ i = i0], [CSIMPNAMEDFORWARD : oelem, intlista, lel, ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPNAMEDSEQ : int-abs, , lels-04, ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (r0 -- j ', val, r -- i ', st)]]