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Proof step 3 from proof in-put-rkvs-mode (conclusion)

⊦ r ≠ jvmref → (_mode ∈ st[((r -- sk) × val) ' + rkvs] ↔ _mode ∈ st[rkvs])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ st[(rk × val) ' + rkvs] = (st[rk, val][rkvs])
Proof step 2:
⊦ rk ∈ st[rkvs] ↔ rk ∈ st ∨ rk ∈ rkvs

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ jvmref → _mode ≠ r -- sk], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPSEQ : ⊦ (rkvs + rkvs0) + rkvs1 = rkvs + rkvs0 + rkvs1])]]