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Proof step 38 from proof onlymod-is-update (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
(st1 -- (r0 -- sk))[rk] = (update(r0, fis, st0 -- (r0 -- sk))[rk]), rk ∈ st1 -- (r0 -- sk) ↔ rk ∈ update(r0, fis, st0 -- (r0 -- sk)), # st0 = m + 1, 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]) ⊦ st0 = ∅, st0[r0 -- sk] = st1[r0 -- sk], rk ∈ st1 ↔ rk = r0 -- sk ∨ rk ∈ update(r0, fis, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]