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Proof step 58 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. (rk ∈ st1 -- (r0 -- sk) ↔ rk ∈ update(r0, fis, st0 -- (r0 -- sk))) ∧ (st1 -- (r0 -- sk))[rk] = (update(r0, fis, st0 -- (r0 -- sk))[rk]) ⊦ st1[rk] = ((rk = r0 -- sk ⊃ st1[r0 -- sk]; update(r0, fis, st0)[rk])), st0[r0 -- sk] = st1[r0 -- sk], st0 = ∅

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 57:
rk ≠ 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]) ⊦ st1[rk] = (update(r0, fis, st0)[rk]), st0[r0 -- sk] = st1[r0 -- sk], st0 = ∅

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]