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Proof step 4 from proof update-mode (previous step)

∀ r, st. r = jvmref ∨ (update(r, fis0, st)[_mode]) = st[_mode] ⊦ r = jvmref, (update(r, (sk × val) ' + fis0, st)[_mode]) = st[_mode]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ update(r, (sk × val) ' + fis, st) = (update(r, fis, st)[r -- sk, val])
Proof step 3:
∀ r, st. r = jvmref ∨ (update(r, fis0, st)[_mode]) = st[_mode] ⊦ r = jvmref, (update(r, fis0, st)[_mode]) = st[_mode]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ jvmref → _mode ≠ r -- sk], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1])]]