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Proof step 20 from proof init-put-23 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
rk .ref = jvmref, rk .key .fs .type = void_type, rk .key .fs .field = `initstate' .field, is_fskey(rk .key), rk ∈ st, ∀ rk0. rk0 ∈ st ∧ rk0 .ref = jvmref ∧ ¬ is_indexkey(rk0 .key) ∧ rk0 .key .fs .type = void_type ∧ rk0 .key .fs .field = `initstate' .field → st[rk0] ≠ initval(undone) ∧ st[rk0] ≠ initval(error) ⊦ r = jvmref, rk = r -- sk, _uninit ∈ st, st[rk] ≠ initval(undone) ∧ st[rk] ≠ initval(error)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ (r -- sk) .ref = r], [CSIMPSEQ : ⊦ (r -- sk) .key = sk], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)])]]