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Proof step 8 from proof okstore-02 (previous step)

_mode ∈ st[r -- sk, val] ∧ _out ∈ st[r -- sk, val] ∧ (∀ r0. r0 ≠ jvmref ∧ r0 ∈ st[r -- sk, val] → r0 -- _type ∈ st[r -- sk, val] ∧ is_typevalue(st[r -- sk, val][r0 -- _type])), jvmref ∈ st ⊦ r = jvmref, (r -- _type ∈ st ∨ _type = sk) ∧ is_typevalue((_type = sk ⊃ val; st[r -- _type]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
_mode ∈ st[r -- sk, val], _out ∈ st[r -- sk, val], jvmref ∈ st, ∀ r0. r0 ≠ jvmref ∧ (r0 = r ∨ r0 ∈ st) → r0 -- _type ∈ st[r -- sk, val] ∧ is_typevalue(((r0 = r ∧ _type = sk) ⊃ val; st[r0 -- _type])) ⊦ r = jvmref, (r -- _type ∈ st ∨ _type = sk) ∧ is_typevalue((_type = sk ⊃ val; st[r -- _type]))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ r ∈ st[r0 -- sk, val] ↔ r = r0 ∨ r ∈ st])]]