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Proof step 46 from proof sharing-pathex-field-self (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(`docs2store', 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 = [], fits(st[refs0 .last -- (fs ' ' + sks)] .refval, fs ' ' + sks, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
⊦ sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks]
Proof step 45:
sks ≠ [], 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(`docs2store', 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 = [], fits(st[st[refs0 .last -- fs '] .refval -- sks] .refval, fs ' ' + sks, st)

Rule argument

[speclemmaarg: ,sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks] ,[sks, sk, r, st] → [sks, fs ', refs0 .last, st] ,F ,storefuns , ,lookup-rec-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ st[r -- []] = refval(r)], [CSIMPSEQ : ⊦ refval(r) = refval(r0) ↔ r = r0], [CSIMPSEQ : ⊦ # [] = 0], [CSIMPSEQ : ⊦ # refs = 0 ↔ refs = []])], [EXTRATERMS : (sks, fs ', refs0 .last, st)]]