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Proof step 25 from proof onlymod-is-update (previous step)

st1 = (update(r0, fis, st0)[r0 -- sk, st1[r0 -- sk]]), # st0 = m + 1, st1 -- (r0 -- sk) = update(r0, fis, st0 -- (r0 -- sk)), r0 -- sk ∈ st1, r0 -- sk ∈ st0, onlyModified(r0, st0, st1), r0 ∈ st1, r0 ∈ st0, validFields(r0, fis, st0 -- (r0 -- sk)) ⊦ st0[r0 -- sk] = st1[r0 -- sk], st0 = ∅, validFields(r0, (sk × st1[r0 -- sk]) ' + fis, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ validFields(r, (sk × val) ' + fis, st) ↔ validFields(r, fis, st) ∧ sk ≠ _length ∧ sk ≠ _type ∧ r -- sk ∈ st ∧ ¬ sk ∈ fis
Proof step 24:
st1 = (update(r0, fis, st0)[r0 -- sk, st1[r0 -- sk]]), # st0 = m + 1, st1 -- (r0 -- sk) = update(r0, fis, st0 -- (r0 -- sk)), r0 -- sk ∈ st1, r0 -- sk ∈ st0, onlyModified(r0, st0, st1), r0 ∈ st1, r0 ∈ st0, validFields(r0, fis, st0 -- (r0 -- sk)) ⊦ st0[r0 -- sk] = st1[r0 -- sk], st0 = ∅, validFields(r0, fis, st0) ∧ sk ≠ _length ∧ sk ≠ _type ∧ r0 -- sk ∈ st0 ∧ ¬ sk ∈ fis

Rule argument

[crewrite-arg: validFields-rec , F , [st, fis, val, sk, r] → [st0, fis, st1[r0 -- sk], sk, r0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, fis, st1[r0 -- sk], sk, r0)]]