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Proof step 9 from proof inv-map (previous step)

err0 = ESUCCESS, m < # avols[v], ebm-cons(avols), v ∈ avols, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪avols[v][m] := mapped(emptyleb, 0)⟫ ebm-cons(avols), avols[v][m].mapped?

Heuristic symbolic execution applied rule assign right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ ⌊ESUCCESS⌋ ; (s)%⊦ v ∈ avols ∧ m < # avols[v] ∧ ebm-cons(avols) → ( ebm-cons(avols[v, avols[v][m, leb]]) ↔ valid-leb(avols[v][m]) → valid-leb(leb)); (ss)%⊦ valid-leb(leb) ↔ leb.mapped? → # leb.data = LEB_SIZE ∧ leb.fill ≤ LEB_SIZE ∧ is-aligned(leb.fill, EB_PAGE_SIZE) ∧ range=(leb.data, leb.fill, emptyleb, 0, LEB_SIZE - leb.fill); (s)% ⊦ mapped(buf, m).mapped?; (s)% ⊦ mapped(buf, m).data = buf; (s)% ⊦ # emptyleb = LEB_SIZE; (s)% ⊦ mapped(buf, m).fill = m; (s)% ⊦ 0 ≤ m; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ is-aligned(0, n); (s)% ⊦ m - 0 = m; (s)% ⊦ range=(buf, n, buf, n, m) ↔ n + m ≤ # buf; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m; (s)