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Proof step 13 from proof fits-put-other (previous step)

st[r -- (sk0 ' + sks2)] .refval = st[r1 -- sks] .refval, st[r -- sk0] = refval(r1), sks2 + sk ' ⊑ sks, is_classtype(st[r -- _type] .type) → sk0 ∈ instfields(st[r -- _type] .type .class), r ≠ st[r1 -- sks] .refval ∨ sk0 ≠ sk ⊦ st[r1 -- sks2] .refval = st[r1 -- sks] .refval, r = jvmref, sk = _length, sk = _type, (is_arraytype(st[r -- _type] .type) → is_indexkey(sk0) ∧ 0 ≤ sk0 .index ∧ sk0 .index < st[r -- _length] .intval) ∧ fits(r1, sks + sk ' + sks1, st[st[r1 -- sks] .refval -- sk, val]) ↔ (is_arraytype(st[r -- _type] .type) → ¬ is_fskey(sk0) ∧ ¬ sk0 .index < 0 ∧ ¬ st[r -- _length] .intval ≤ sk0 .index) ∧ fits(r1, sks + sk ' + sks1, st), fits(r1, sks + sk ' + sks1, st[st[r1 -- sks] .refval -- sk, val]) ↔ fits(r1, sks + sk ' + sks1, st), sks = []

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [sks2, sk0, r, st] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, storekeys, app, ⊦ sks + [] = sks], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : storefuns, , lookup-one, ⊦ st[r -- sk '] = st[r -- sk]], [CSIMPNAMEDSEQ : storefuns, , lookup-empty, ⊦ st[r -- []] = refval(r)], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r], [CSIMPNAMEDSEQ : list, storekeys, Nil, ⊦ [] + sks = sks])], [EXTRATERMS : (sks2, sk0, r, st)]]