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Proof step 39 from proof at-put-prim (previous step)

st[r0 -- sk0] = refval(r1), is_referencevalue(st[r0 -- (sk0 ' + sks0)]), fits(r1, sks0, st), is_classtype(st[r0 -- _type] .type) → sk0 ∈ instfields(st[r0 -- _type] .type .class), is_arraytype(st[r0 -- _type] .type) → is_indexkey(sk0) ∧ 0 ≤ sk0 .index ∧ sk0 .index < st[r0 -- _length] .intval, ∀ st, r0, r, sk, val, str. is_referencevalue(st[r0 -- sks0]) ∧ fits(r0, sks0, st) → sks0 = [] ∨ (st[r -- sk, val][r0 -- sks0]) = st[r0 -- sks0] ∨ is_referencevalue(st[r -- sk]) ∨ junkref(str, r, st) ∨ junkref(str, r0, st) ⊦ (st[r -- sk, val][r0 -- (sk0 ' + sks0)]) = st[r0 -- (sk0 ' + sks0)], r0 = jvmref, is_referencevalue(st[r -- sk]), junkref(str, r, st), junkref(str, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks]
Proof step 6:
¬ sks0 ≠ [], st[r0 -- sk0] = refval(r1), is_referencevalue(st[r0 -- (sk0 ' + sks0)]), fits(r1, sks0, st), is_classtype(st[r0 -- _type] .type) → sk0 ∈ instfields(st[r0 -- _type] .type .class), is_arraytype(st[r0 -- _type] .type) → is_indexkey(sk0) ∧ 0 ≤ sk0 .index ∧ sk0 .index < st[r0 -- _length] .intval, ∀ st, r0, r, sk, val, str. is_referencevalue(st[r0 -- sks0]) ∧ fits(r0, sks0, st) → sks0 = [] ∨ (st[r -- sk, val][r0 -- sks0]) = st[r0 -- sks0] ∨ is_referencevalue(st[r -- sk]) ∨ junkref(str, r, st) ∨ junkref(str, r0, st) ⊦ (st[r -- sk, val][r0 -- (sk0 ' + sks0)]) = st[r0 -- (sk0 ' + sks0)], r0 = jvmref, is_referencevalue(st[r -- sk]), junkref(str, r, st), junkref(str, r0, st)
Proof step 38:
sks0 ≠ [], st[r0 -- sk0] = refval(r1), is_referencevalue(st[st[r0 -- sk0] .refval -- sks0]), fits(r1, sks0, st), is_classtype(st[r0 -- _type] .type) → sk0 ∈ instfields(st[r0 -- _type] .type .class), is_arraytype(st[r0 -- _type] .type) → is_indexkey(sk0) ∧ 0 ≤ sk0 .index ∧ sk0 .index < st[r0 -- _length] .intval, ∀ st, r0, r, sk, val, str. is_referencevalue(st[r0 -- sks0]) ∧ fits(r0, sks0, st) → sks0 = [] ∨ (st[r -- sk, val][r0 -- sks0]) = st[r0 -- sks0] ∨ is_referencevalue(st[r -- sk]) ∨ junkref(str, r, st) ∨ junkref(str, r0, st) ⊦ (st[r -- sk, val][r0 -- (sk0 ' + sks0)]) = st[st[r0 -- sk0] .refval -- sks0], r0 = jvmref, is_referencevalue(st[r -- sk]), junkref(str, r, st), junkref(str, r0, st)

Rule argument

[x0lemmaarg: spec-name: storefuns instance-name: lemma-name: lookup-rec-01 antecedent: succedent: sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks] substlist: [sks, sk, r, st] → [sks0, sk0, r0, st] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 1, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sks0, sk0, r0, st)]]