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Proof step 16 from proof onlymod-sym-01 (previous step)

r -- _length ∈ st0 → st0[r -- _length] = st[r -- _length], r -- _type ∈ st0 → st0[r -- _type] = st[r -- _type], ∀ r0, sk. r0 ≠ r → st0[r0 -- sk] = st[r0 -- sk], ∀ rk. rk ∈ st0 ↔ rk ∈ st ⊦ onlyModified(r, st, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 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 15:
r -- _length ∈ st0 → st0[r -- _length] = st[r -- _length], r -- _type ∈ st0 → st0[r -- _type] = st[r -- _type], ∀ r0, sk. r0 ≠ r → st0[r0 -- sk] = st[r0 -- sk], ∀ rk. rk ∈ st0 ↔ rk ∈ st ⊦ (∀ 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])

Rule argument

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

Additional information

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