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Proof step 42 from proof isarray-put-array-badindex (previous step)

st[r0 -- _type] = typeval(mkarraytype(ty)), 0 ≤ st[r0 -- _length] .intval, is_integervalue(st[r0 -- _length]), r0 ∈ st, r0 -- _type ∈ st, i < 0 ⊦ r0 -- _length ∈ st[r -- i ', val] ∧ is_arrayref(r0, st[r0 -- _length] .intval, st[r -- i ', val]) ∧ (∀ j. ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j → okval(st[r -- i ', val][r0 -- j '], ty)) ↔ okreftype(refval(r0), mkarraytype(ty), st) ∧ r0 -- _length ∈ st ∧ is_arrayref(r0, st[r0 -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r0 -- _length] .intval → okval(st[r0 -- j '], ty)), r0 = jvmref

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 41:
st[r0 -- _length] = intval(i0), st[r0 -- _type] = typeval(mkarraytype(ty)), 0 ≤ i0, is_integervalue(st[r0 -- _length]), r0 ∈ st, r0 -- _type ∈ st, i < 0 ⊦ r0 -- _length ∈ st[r -- i ', val] ∧ is_arrayref(r0, i0, st[r -- i ', val]) ∧ (∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- i ', val][r0 -- j '], ty)) ↔ okreftype(refval(r0), mkarraytype(ty), st) ∧ r0 -- _length ∈ st ∧ is_arrayref(r0, i0, st) ∧ (∀ j. 0 ≤ j ∧ j < i0 → okval(st[r0 -- j '], ty)), r0 = jvmref

Rule argument

[x0lemmaarg: spec-name: javavalue instance-name: lemma-name: elim-02 antecedent: succedent: is_integervalue(val) → (i = val .intval ↔ val = intval(i)) substlist: [val, i] → [st[r0 -- _length], i0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_integervalue(val) → ( i = val .intval ↔ val = intval(i))])], [EXTRATERMS : (st[r0 -- _length], i0)]]