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Proof step 8 from proof onlymod-init-02 (previous step)

st[jvmref -- mkfs(class, void_type, `initstate' .field) '] = initval(error), jvmref ∈ st, jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st, ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st0 ∨ st0[jvmref -- mkfs(class, void_type, `initstate' .field) '] ≠ initval(error), r -- _length ∈ st → st[r -- _length] = st0[r -- _length], r -- _type ∈ st → st[r -- _type] = st0[r -- _type], ∀ r0, sk. r0 ≠ r → st[r0 -- sk] = st0[r0 -- sk], ∀ rk. rk ∈ st ↔ rk ∈ st0 ⊦ r = jvmref

User applied rule case distinction

And obtained the following new goals

Proof step 5:
¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st0, st[jvmref -- mkfs(class, void_type, `initstate' .field) '] = initval(error), jvmref ∈ st, jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st, r -- _length ∈ st → st[r -- _length] = st0[r -- _length], r -- _type ∈ st → st[r -- _type] = st0[r -- _type], ∀ r0, sk. r0 ≠ r → st[r0 -- sk] = st0[r0 -- sk], ∀ rk. rk ∈ st ↔ rk ∈ st0 ⊦ r = jvmref
Proof step 7:
st0[jvmref -- mkfs(class, void_type, `initstate' .field) '] ≠ initval(error), st[jvmref -- mkfs(class, void_type, `initstate' .field) '] = initval(error), jvmref ∈ st, jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st, r -- _length ∈ st → st[r -- _length] = st0[r -- _length], r -- _type ∈ st → st[r -- _type] = st0[r -- _type], ∀ r0, sk. r0 ≠ r → st[r0 -- sk] = st0[r0 -- sk], ∀ rk. rk ∈ st ↔ rk ∈ st0 ⊦ r = jvmref

Rule argument

[CASEDARG : pos: left 4, ()]

Additional information

[[CONCRETESIMPRULES : ()]]