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Proof step 40 from proof lookup-statfield (previous step)

st[r -- sk0] .refval = jvmref ∨ junkref(str, st[r -- sk0] .refval, st), fits(r, sk0 ' + sks0, st), ∀ r, st, sk, val, str. fits(r, sks0, st) → r = jvmref ∨ (st[jvmref -- sk, val][r -- sks0]) = st[r -- sks0] ∨ junkref(str, r, st) ⊦ sks0 = [], (st[jvmref -- sk, val][st[r -- sk0] .refval -- sks0]) = st[st[r -- sk0] .refval -- sks0], r = jvmref, junkref(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ fits(r, sk ' + sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ (is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval) ∧ fits(st[r -- sk] .refval, sks, st)
Proof step 39:
st[r -- sk0] .refval = jvmref ∨ junkref(str, st[r -- sk0] .refval, st), r ≠ jvmref ∧ is_referencevalue(st[r -- sk0]) ∧ (is_classtype(st[r -- _type] .type) → sk0 ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sk0) ∧ 0 ≤ sk0 .index ∧ sk0 .index < st[r -- _length] .intval) ∧ fits(st[r -- sk0] .refval, sks0, st), ∀ r, st, sk, val, str. fits(r, sks0, st) → r = jvmref ∨ (st[jvmref -- sk, val][r -- sks0]) = st[r -- sks0] ∨ junkref(str, r, st) ⊦ sks0 = [], (st[jvmref -- sk, val][st[r -- sk0] .refval -- sks0]) = st[st[r -- sk0] .refval -- sks0], r = jvmref, junkref(str, r, st)

Rule argument

[crewrite-arg: fits-storekeys-rec , F , [st, sks, sk, r] → [st, sks0, sk0, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, sks0, sk0, r)]]