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Proof step 21 from proof init-put-06 (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 11:
¬ _uninit ∈ st ∧ (∀ rk. (rk = r -- i ' ∨ rk ∈ st) ∧ rk .ref = jvmref ∧ ¬ is_indexkey(rk .key) ∧ rk .key .fs .type = void_type ∧ rk .key .fs .field = `initstate' .field → ((rk = r -- i ' ⊃ val; st[rk])) ≠ initval(undone) ∧ ((rk = r -- i ' ⊃ val; st[rk])) ≠ initval(error)) ⊦ ¬ _uninit ∈ st ∧ (∀ 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))
Proof step 20:
¬ _uninit ∈ st ∧ (∀ 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)) ⊦ ¬ _uninit ∈ st ∧ (∀ rk. (rk = r -- i ' ∨ rk ∈ st) ∧ rk .ref = jvmref ∧ ¬ is_indexkey(rk .key) ∧ rk .key .fs .type = void_type ∧ rk .key .fs .field = `initstate' .field → ((rk = r -- i ' ⊃ val; st[rk])) ≠ initval(undone) ∧ ((rk = r -- i ' ⊃ val; st[rk])) ≠ initval(error))

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]