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Proof step 53 from proof onlymod-is-update (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
⊦ r ≠ r0 → (update(r0, fis, st)[r -- sk]) = st[r -- sk]
Proof step 41:
⊦ r ≠ r0 → (r -- sk ∈ update(r0, fis, st) ↔ r -- sk ∈ st)
Proof step 52:
st1[r0 -- sk0] = (update(r0, fis, st0 -- (r0 -- sk))[r0 -- sk0]), r0 -- sk0 ∈ st1 ↔ r0 -- sk0 ∈ update(r0, fis, st0 -- (r0 -- sk)), # st0 = m + 1, 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]) ⊦ sk0 = sk, st1[r0 -- sk0] = (update(r0, fis, st0)[r0 -- sk0]), st0[r0 -- sk] = st1[r0 -- sk], st0 = ∅

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ rk ∈ st ∧ onlyModified(r, st, st0) → ¬ rk ∈ st0], [CSIMPSEQ : ⊦ rk ∈ st -- rk0 ↔ rk ≠ rk0 ∧ rk ∈ st], [CSIMPSEQ : ⊦ r ≠ r0 → (st -- (r -- sk))[r0 -- sk0] = st[r0 -- sk0]], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]