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Proof step 38 from proof crash-neutral-write (previous step)

v0 ∈ avols ↔ v0 ∈ avols0, m2 < # avols[v], ebm-cons(avols), ebm-cons(avols0), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), v ∈ avols, m1 + n ≤ LEB_SIZE, n + n2 ≤ # buf, v0 ∈ avols0 → # avols[v0] = # avols0[v0] ∧ (∀ m. m < # avols[v0] ∧ avols[v0][m] ≠ unmapped → (avols[v0][m] = erased → avols0[v0][m] = erased) ∧ (avols[v0][m].mapped? → avols0[v0][m] = avols[v0][m])) ⊦ n = 0, v0 = v, avols[v][m2].mapped?, (v0 ∈ avols[v, avols[v][m2, unmapped]] ↔ v0 ∈ avols0) ∧ ( v0 ∈ avols[v, avols[v][m2, unmapped]] → # avols[v, avols[v][m2, unmapped]][v0] = # avols0[v0] ∧ ( m < # avols[v, avols[v][m2, unmapped]][v0] ∧ avols[v, avols[v][m2, unmapped]][v0][m] ≠ unmapped → (avols[v, avols[v][m2, unmapped]][v0][m] = erased → avols0[v0][m] = erased) ∧ (avols[v, avols[v][m2, unmapped]][v0][m].mapped? → avols0[v0][m] = avols[v, avols[v][m2, unmapped]][v0][m])))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
# avols[v0] = # avols0[v0], m < # avols0[v0], m2 < # avols[v], ebm-cons(avols), ebm-cons(avols0), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), v0 ∈ avols0, v0 ∈ avols, v ∈ avols, m1 + n ≤ LEB_SIZE, n + n2 ≤ # buf, ∀ m. m < # avols0[v0] ∧ avols[v0][m] ≠ unmapped → (avols[v0][m] = erased → avols0[v0][m] = erased) ∧ (avols[v0][m].mapped? → avols0[v0][m] = avols[v0][m]) ⊦ avols[v0][m] = unmapped, n = 0, v0 = v, avols[v][m2].mapped?, (avols[v0][m] = erased → avols0[v0][m] = erased) ∧ (avols[v0][m].mapped? → avols0[v0][m] = avols[v0][m])

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ v ≠ v0 → avols[v0, evol][v] = avols[v]; (s)% ⊦ v ≠ v0 → (v ∈ avols[v0, evol] ↔ v ∈ avols); (s)