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Proof step 9 from proof okstore-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
_out ∈ st, _mode ∈ st, _out ∈ st[r -- sk, val], _mode ∈ st[r -- sk, val], ∀ r. r ≠ jvmref ∧ r ∈ st → r -- _type ∈ st ∧ is_typevalue(st[r -- _type]), ∀ 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, is_typevalue((_type = sk ⊃ val; st[r -- _type])) ∧ (r -- _type ∈ st ∨ _type = sk)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]