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Proof step 8 from proof onlymod-put (previous step)

onlyModified(r, st, st0), r -- sk ∈ st, r ∈ st ⊦ sk = _length, sk = _type, (rk ∈ st → rk = r -- sk ∨ rk ∈ st0) ∧ (r0 ≠ r → st[r0 -- sk0] = st0[r0 -- sk0]) ∧ (r -- _type ∈ st → st[r -- _type] = st0[r -- _type]) ∧ (r -- _length ∈ st → st[r -- _length] = st0[r -- _length])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ onlyModified(r, st1, st2) ↔ (∀ rk. rk ∈ st1 ↔ rk ∈ st2) ∧ (∀ r0, sk. r0 ≠ r → st1[r0 -- sk] = st2[r0 -- sk]) ∧ (r -- _type ∈ st1 → st1[r -- _type] = st2[r -- _type]) ∧ (r -- _length ∈ st1 → st1[r -- _length] = st2[r -- _length])
Proof step 7:
(∀ rk. rk ∈ st ↔ rk ∈ st0) ∧ (∀ r0, sk. r0 ≠ r → st[r0 -- sk] = st0[r0 -- sk]) ∧ (r -- _type ∈ st → st[r -- _type] = st0[r -- _type]) ∧ (r -- _length ∈ st → st[r -- _length] = st0[r -- _length]), r -- sk ∈ st, r ∈ st ⊦ sk = _length, sk = _type, (rk ∈ st → rk = r -- sk ∨ rk ∈ st0) ∧ (r0 ≠ r → st[r0 -- sk0] = st0[r0 -- sk0]) ∧ (r -- _type ∈ st → st[r -- _type] = st0[r -- _type]) ∧ (r -- _length ∈ st → st[r -- _length] = st0[r -- _length])

Rule argument

[crewrite-arg: onlyModified, F, [st2, st1, r] → [st0, st, r]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, st, r)]]