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Proof step 44 from proof fits-superset (previous step)

st[r -- sk] = refval(r0), is_array(str, r, st), st ⊆ st0, fits(r0, sks0, st), is_arraytype(st[r -- _type] .type), is_indexkey(sk), sk .index < st[r -- _length] .intval, 0 ≤ sk .index, 0 < st[r -- _length] .intval, ∀ st, st0, r, str. st ⊆ st0 ∧ fits(r, sks0, st) → junkref(str, r, st) ∨ fits(r, sks0, st0) ⊦ r = jvmref, junkref(str, r, st), is_referencevalue(st0[r -- sk]) ∧ (is_classtype(st0[r -- _type] .type) → sk ∈ instfields(st0[r -- _type] .type .class)) ∧ (is_arraytype(st0[r -- _type] .type) → ¬ st0[r -- _length] .intval ≤ sk .index) ∧ fits(st0[r -- sk] .refval, sks0, st0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 43:
sk = i ', st[r -- sk] = refval(r0), is_array(str, r, st), st ⊆ st0, fits(r0, sks0, st), is_arraytype(st[r -- _type] .type), is_indexkey(sk), i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval, ∀ st, st0, r, str. st ⊆ st0 ∧ fits(r, sks0, st) → junkref(str, r, st) ∨ fits(r, sks0, st0) ⊦ r = jvmref, junkref(str, r, st), is_referencevalue(st0[r -- sk]) ∧ (is_classtype(st0[r -- _type] .type) → sk ∈ instfields(st0[r -- _type] .type .class)) ∧ (is_arraytype(st0[r -- _type] .type) → ¬ st0[r -- _length] .intval ≤ i) ∧ fits(st0[r -- sk] .refval, sks0, st0)

Rule argument

[speclemmaarg: ,is_indexkey(sk) → (i = sk .index ↔ sk = i ') ,[sk, i] → [sk, i] ,T ,storekey , ,elim-04 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_indexkey(sk) → (i = sk .index ↔ sk = i ')])], [EXTRATERMS : (sk, i)]]