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Proof step 10 from proof init-put-nonvoid (previous step)

tdname∃(str, class0), ¬ jvmref -- mkfs(class0, void_type, `initstate' .field) ' ∈ st ∨ (st[r -- mkfs(class, ty, fieldvar) ', val][jvmref -- mkfs(class0, void_type, `initstate' .field) ']) ≠ initval(error), ¬ jvmref -- mkfs(class0, void_type, `initstate' .field) ' ∈ st ∨ (st[r -- mkfs(class, ty, fieldvar) ', val][jvmref -- mkfs(class0, void_type, `initstate' .field) ']) ≠ initval(undone), jvmref -- mkfs(class0, void_type, `initstate' .field) ' ∈ st[r -- mkfs(class, ty, fieldvar) ', val] ∨ _uninit ≠ r -- mkfs(class, ty, fieldvar) ' ∧ ¬ _uninit ∈ st ⊦ ty = void_type, (¬ jvmref -- mkfs(class0, void_type, `initstate' .field) ' ∈ st ∨ st[jvmref -- mkfs(class0, void_type, `initstate' .field) '] ≠ initval(error)) ∧ (¬ jvmref -- mkfs(class0, void_type, `initstate' .field) ' ∈ st ∨ st[jvmref -- mkfs(class0, void_type, `initstate' .field) '] ≠ initval(undone)) ∧ (jvmref -- mkfs(class0, void_type, `initstate' .field) ' ∈ st ∨ ¬ _uninit ∈ st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]

Rule argument

[x0lemmaarg: spec-name: store instance-name: javastore lemma-name: At-other antecedent: succedent: rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] substlist: [rk, val, rk0, st] → [jvmref -- mkfs(class0, void_type, `initstate' .field) ', val, r -- mkfs(class, ty, fieldvar) ', st] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 1, 1, 1, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : refkey, , inj-01, ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPNAMEDSEQ : storekey, , inj-03, ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPNAMEDSEQ : fieldspec, , inj-01, ⊦ mkfs(class1, ty, fieldvar) = mkfs (class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)], [CSIMPNAMEDSEQ : store, javastore, In-insert, ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPNAMEDSEQ : refkey, , inj, ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPNAMEDSEQ : fieldspec, , inj, ⊦ mkfs(class, ty, fieldvar) = mkfs (class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0])], [EXTRATERMS : ( jvmref -- mkfs(class0, void_type, `initstate' .field) ', val, r -- mkfs(class, ty, fieldvar) ', st)]]