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Proof step 44 from proof sharing-pathex-field-self-01 (previous step)

st[r -- sks] = refval(refs0 .last), st[refs0 .last -- _type] .type = mkclasstype(class), st[refs0 .last -- fs '] = refval(r), # sks = # refs0, fs ' ∈ instfields(class), validrefs(str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st), fits(r, sks, st), ∀ n. n ≠ 0 ∧ ¬ # refs0 < n → st[r -- firstn(n, sks)] .refval = (r ' + refs0)[n] ⊦ refs0 .last = jvmref, refs0 = [], sks = [], fits(refs0 .last, fs ' ' + sks, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: sharing instance-name: lemma-name: fits-storekeys-rec antecedent: succedent: 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) substlist: [st, sks, sk, r] → [st, sks, fs ', refs0 .last] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : storekey, , test-07, ⊦ ¬ is_indexkey(fs ')], [CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))], [CSIMPNAMEDSEQ : javatype, , test-10, ⊦ is_classtype (mkclasstype(class))], [CSIMPNAMEDSEQ : javatype, , sel-02, ⊦ mkclasstype(class) .class = class], [CSIMPNAMEDSEQ : javatype, , test-28, ⊦ ¬ is_arraytype (mkclasstype(class))], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r])], [EXTRATERMS : (st, sks, fs ', refs0 .last)]]