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Proof step 68 from proof unchanged-lookup-list-generic (previous step)

unchanged(str, r, st, st0), is_referencevalue(st0[r -- sk]), fits(st0[r -- sk] .refval, sks0, st0), fits(st[r -- sk] .refval, sks0, st), is_referencevalue(st[r -- sk]), is_classtype(st0[r -- _type] .type) → sk ∈ instfields(st0[r -- _type] .type .class), is_arraytype(st0[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st0[r -- _length] .intval, ∀ r, st0, st, str. fits(r, sks0, st0) ∧ fits(r, sks0, st) ∧ unchanged(str, r, st, st0) → st[r -- sks0] = st0[r -- sks0] ∨ junkref(str, r, st) ∨ junkref(str, r, st0), is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval, is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class) ⊦ r = jvmref, sks0 = [], st[st[r -- sk] .refval -- sks0] = st0[st0[r -- sk] .refval -- sks0], junkref(str, r, st), junkref(str, r, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ unchanged(str, r, st, st0) ∧ path∃(str, r, r0, st) ∧ r0 ≠ jvmref ∧ (is_classtype(st[r0 -- _type] .type) → sk ∈ instfields(st[r0 -- _type] .type .class)) ∧ (is_arraytype(st[r0 -- _type] .type) → sk = _length ∨ is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r0 -- _length] .intval) → st[r0 -- sk] = st0[r0 -- sk]
Proof step 67:
unchanged(str, r, st, st0) ∧ path∃(str, r, r, st) ∧ r ≠ jvmref ∧ (is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → sk = _length ∨ is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval), unchanged(str, r, st, st0), is_referencevalue(st0[r -- sk]), fits(st0[r -- sk] .refval, sks0, st0), fits(st0[r -- sk] .refval, sks0, st), is_referencevalue(st0[r -- sk]), is_classtype(st0[r -- _type] .type) → sk ∈ instfields(st0[r -- _type] .type .class), is_arraytype(st0[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st0[r -- _length] .intval, ∀ r, st0, st, str. fits(r, sks0, st0) ∧ fits(r, sks0, st) ∧ unchanged(str, r, st, st0) → st[r -- sks0] = st0[r -- sks0] ∨ junkref(str, r, st) ∨ junkref(str, r, st0), is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval, is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class) ⊦ r = jvmref, sks0 = [], st[st0[r -- sk] .refval -- sks0] = st0[st0[r -- sk] .refval -- sks0], junkref(str, r, st), junkref(str, r, st0)

Rule argument

[x0lemmaarg: spec-name: pointers instance-name: lemma-name: unchanged-lookup-generic antecedent: succedent: unchanged(str, r, st, st0) ∧ path∃(str, r, r0, st) ∧ r0 ≠ jvmref ∧ ( is_classtype(st[r0 -- _type] .type) → sk ∈ instfields(st[r0 -- _type] .type .class)) ∧ ( is_arraytype(st[r0 -- _type] .type) → sk = _length ∨ is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r0 -- _length] .intval) → st[r0 -- sk] = st0[r0 -- sk] substlist: [str, r, st, st0, r0, sk] → [str, r, st, st0, r, sk] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 2, 1, 0, 1, 1, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : cyclic, , pathex-one, ⊦ path∃(str, r, r, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st)], [CSIMPNAMEDSEQ : storekey, , test, ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPNAMEDSEQ : int-abs, , lels-01, ⊦ ¬ i ≤ j ↔ j < i], [CSIMPNAMEDSEQ : int-abs, , lels, ⊦ ¬ i < j ↔ j ≤ i], [CSIMPNAMEDSEQ : junkrefs, , junkref-not-valid-01, ⊦ ¬ is_valid_ref(str, r, st) ∧ r ≠ jvmref → junkref(str, r, st)], [CSIMPNAMEDSEQ : addfuns, , is_valid_ref-array-01, ⊦ is_arraytype (st[r -- _type] .type) ∧ r ≠ jvmref → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))], [CSIMPNAMEDSEQ : javatype, , diff-01, ⊦ is_arraytype(ty) → ¬ is_classtype(ty)], [CSIMPNAMEDSEQ : addfuns, , instfields-index-01, ⊦ is_indexkey(sk) → ¬ sk ∈ instfields(class)], [CSIMPNAMEDSEQ : int-abs, , zero-gels-04, ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPNAMEDSEQ : junkrefs, , junkref-bad-type, ⊦ ¬ is_classtype (st[r -- _type] .type) ∧ ¬ is_arraytype (st[r -- _type] .type) → ( junkref(str, r, st) ↔ r ≠ jvmref)], [CSIMPNAMEDSEQ : storekey, , test-02, ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPNAMEDSEQ : int-abs, , lels-04, ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPNAMEDSEQ : int-abs, , lels-03, ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (str, r, st, st0, r, sk)]]