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Proof step 48 from proof sharing-pathex-field-self (previous step)

# sks = # refs0, st[refs0 .last -- fs '] = refval(r), st[refs0 .last -- _type] .type = mkclasstype(class), st[r -- sks] = refval(refs0 .last), fits(r, sks, st), validrefs(`docs2store', r ' + refs0, mkclasstype(`java.lang.Object' .class), st), fs ' ∈ instfields(class), ∀ n. n ≠ 0 ∧ ¬ # refs0 < n → st[r -- firstn(n, sks)] .refval = (r ' + refs0)[n] ⊦ fits(refs0 .last, fs ' ' + sks, st) ∧ fits(st[refs0 .last -- (fs ' ' + sks)] .refval, fs ' ' + sks, st), refs0 = [], refs0 .last = jvmref, fits(refs0 .last, fs ' ' + sks, st) ∧ fits(refs0 .last, fs ' ' + sks, st) ∧ fits(st[refs0 .last -- (fs ' ' + sks)] .refval, fs ' ' + sks, st) ∧ st[refs0 .last -- (fs ' ' + sks)] .refval ≠ jvmref ∧ st[refs0 .last -- (fs ' ' + sks)] = st[refs0 .last -- (fs ' ' + sks + fs ' ' + sks)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ 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 47:
# sks = # refs0, st[refs0 .last -- fs '] = refval(r), st[refs0 .last -- _type] .type = mkclasstype(class), st[r -- sks] = refval(refs0 .last), fits(r, sks, st), validrefs(`docs2store', r ' + refs0, mkclasstype(`java.lang.Object' .class), st), fs ' ∈ instfields(class), ∀ n. n ≠ 0 ∧ ¬ # refs0 < n → st[r -- firstn(n, sks)] .refval = (r ' + refs0)[n] ⊦ refs0 .last ≠ jvmref ∧ is_referencevalue(st[refs0 .last -- fs ']) ∧ (is_classtype(st[refs0 .last -- _type] .type) → fs ' ∈ instfields(st[refs0 .last -- _type] .type .class)) ∧ (is_arraytype(st[refs0 .last -- _type] .type) → is_indexkey(fs ') ∧ 0 ≤ fs ' .index ∧ fs ' .index < st[refs0 .last -- _length] .intval) ∧ fits(st[refs0 .last -- fs '] .refval, sks, st) ∧ fits(st[refs0 .last -- (fs ' ' + sks)] .refval, fs ' ' + sks, st), refs0 = [], refs0 .last = jvmref, refs0 .last ≠ jvmref ∧ is_referencevalue(st[refs0 .last -- fs ']) ∧ (is_classtype(st[refs0 .last -- _type] .type) → fs ' ∈ instfields(st[refs0 .last -- _type] .type .class)) ∧ (is_arraytype(st[refs0 .last -- _type] .type) → is_indexkey(fs ') ∧ 0 ≤ fs ' .index ∧ fs ' .index < st[refs0 .last -- _length] .intval) ∧ fits(st[refs0 .last -- fs '] .refval, sks, st) ∧ refs0 .last ≠ jvmref ∧ is_referencevalue(st[refs0 .last -- fs ']) ∧ (is_classtype(st[refs0 .last -- _type] .type) → fs ' ∈ instfields(st[refs0 .last -- _type] .type .class)) ∧ (is_arraytype(st[refs0 .last -- _type] .type) → is_indexkey(fs ') ∧ 0 ≤ fs ' .index ∧ fs ' .index < st[refs0 .last -- _length] .intval) ∧ fits(st[refs0 .last -- fs '] .refval, sks, st) ∧ fits(st[refs0 .last -- (fs ' ' + sks)] .refval, fs ' ' + sks, st) ∧ st[refs0 .last -- (fs ' ' + sks)] .refval ≠ jvmref ∧ st[refs0 .last -- (fs ' ' + sks)] = st[refs0 .last -- (fs ' ' + sks + fs ' ' + sks)]

Rule argument

[crewrite-arg: fits-storekeys-rec , F , [st, sks, sk, r] → [st, sks, fs ', refs0 .last] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, sks, fs ', refs0 .last)]]