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Proof step 49 from proof onlymod-is-update (previous step)

# st0 = m + 1, st1[r0 -- sk0] = (st0 -- (r0 -- sk))[r0 -- sk0], r0 -- sk ∈ st1, r0 -- sk ∈ st0, onlyModified(r0, st0, st1), r0 ∈ st1, r0 ∈ st0, validFields(r0, fis, st0 -- (r0 -- sk)), ∀ rk. (rk ∈ st1 -- (r0 -- sk) ↔ rk ∈ update(r0, fis, st0 -- (r0 -- sk))) ∧ (st1 -- (r0 -- sk))[rk] = (update(r0, fis, st0 -- (r0 -- sk))[rk]), r0 -- sk0 ≠ r0 -- sk ∧ r0 -- sk0 ∈ st0 → r0 -- sk0 ∈ st1 ⊦ sk0 = sk, st1[r0 -- sk0] = st0[r0 -- sk0], st0[r0 -- sk] = st1[r0 -- sk], st0 = ∅, sk0 ∈ fis

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
# st0 = m + 1, st1[r0 -- sk0] = (st0 -- (r0 -- sk))[r0 -- sk0], r0 -- sk ∈ st1, r0 -- sk ∈ st0, onlyModified(r0, st0, st1), r0 ∈ st1, r0 ∈ st0, validFields(r0, fis, st0 -- (r0 -- sk)), ∀ rk. (rk ∈ st1 -- (r0 -- sk) ↔ rk ∈ update(r0, fis, st0 -- (r0 -- sk))) ∧ (st1 -- (r0 -- sk))[rk] = (update(r0, fis, st0 -- (r0 -- sk))[rk]), r0 -- sk0 ∈ st0 → r0 -- sk0 ∈ st1 ⊦ sk0 = sk, st1[r0 -- sk0] = st0[r0 -- sk0], st0[r0 -- sk] = st1[r0 -- sk], st0 = ∅, sk0 ∈ fis

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0])]]