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Proof step 4 from proof validmode-noval-put (previous step)

st[_mode] = noval ⊦ rk = _mode, _mode ∈ st[rk, val] ∧ validmode(str, st[rk, val][_mode], st[rk, val]) ↔ _mode ∈ st

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
st[_mode] = noval, _mode ∈ st ⊦ rk = _mode, validmode(str, noval, st[rk, val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st])]]