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Proof step 30 from proof inv-format (previous step)

(∅)[default-volid, fill(mkabstractvolume(n), erased)][v][m] = mapped(buf, m0), m < # (∅)[default-volid, fill(mkabstractvolume(n), erased)][v], v ∈ (∅)[default-volid, fill(mkabstractvolume(n), erased)] ⊦ # buf = LEB_SIZE ∧ m0 ≤ LEB_SIZE ∧ is-aligned(m0, EB_PAGE_SIZE) ∧ range=(buf, m0, emptyleb, 0, LEB_SIZE - m0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ v ∈ avols[v0, evol] ↔ v = v0 ∨ v ∈ avols

Rule argument

spec: store, inst: abstract-volumes name: In-insert seq: ⊦ v ∈ avols[v0, evol] ↔ v = v0 ∨ v ∈ avols subst: [evol, v0, avols, v] → [fill(mkabstractvolume(n), erased), default-volid, ∅, v] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ v ∈ ∅; (s)% ⊦ v = v0 → avols[v0, evol][v] = evol; (s)% ⊦ # fill(evol, leb) = # evol; (s)% ⊦ # mkabstractvolume(n) = n; (s)% ⊦ m < n → fill(mkabstractvolume(n), leb)[m] = leb; (s)% ⊦ erased ≠ mapped(buf, m); (s) Used terms: fill(mkabstractvolume(n), erased), default-volid, ∅, v