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

rk .key .fs .field = `initstate' .field, rk .key .fs .type = void_type, rk .ref = jvmref, is_fskey(rk .key), rk ∈ st, ∀ rk. (rk = r -- mkfs(class, ty, fieldvar) ' ∨ rk ∈ st) ∧ rk .ref = jvmref ∧ ¬ is_indexkey(rk .key) ∧ rk .key .fs .type = void_type ∧ rk .key .fs .field = `initstate' .field → ((rk = r -- mkfs(class, ty, fieldvar) ' ⊃ val; st[rk])) ≠ initval(undone) ∧ ((rk = r -- mkfs(class, ty, fieldvar) ' ⊃ val; st[rk])) ≠ initval(error) ⊦ _uninit = r -- mkfs(class, ty, fieldvar) ', ty = void_type, _uninit ∈ st, st[rk] ≠ initval(undone) ∧ st[rk] ≠ initval(error)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
rk = r0 -- sk, sk .fs .field = `initstate' .field, sk .fs .type = void_type, r0 = jvmref, is_fskey(sk), rk ∈ st, ∀ rk. (rk = r -- mkfs(class, ty, fieldvar) ' ∨ rk ∈ st) ∧ rk .ref = jvmref ∧ ¬ is_indexkey(rk .key) ∧ rk .key .fs .type = void_type ∧ rk .key .fs .field = `initstate' .field → ((rk = r -- mkfs(class, ty, fieldvar) ' ⊃ val; st[rk])) ≠ initval(undone) ∧ ((rk = r -- mkfs(class, ty, fieldvar) ' ⊃ val; st[rk])) ≠ initval(error) ⊦ _uninit = r -- mkfs(class, ty, fieldvar) ', ty = void_type, _uninit ∈ st, st[rk] ≠ initval(undone) ∧ st[rk] ≠ initval(error)

Rule argument

[speclemmaarg: ,r = rk .ref ∧ sk = rk .key ↔ rk = r -- sk ,[rk, r, sk] → [rk, r0, sk] ,T ,refkey , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ r = rk .ref ∧ sk = rk .key ↔ rk = r -- sk])], [EXTRATERMS : (rk, r0, sk)]]