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Proof step 61 from proof refine-write (previous step)

LEB_SIZE = (n4 + n) + m1, avols[default-volid][m2] = mapped(buf0, n2), avol = abs(avols[default-volid]), m = m1, m0 = m2, n0 = n, n1 = n3, m2 < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), default-volid ∈ avols, n + m1 ≤ LEB_SIZE, n3 + n ≤ # buf, m1 + n ≤ LEB_SIZE, n2 ≤ m1, m1 ≤ LEB_SIZE, n2 ≤ LEB_SIZE, m0 < # avol → m0 < # avol ∧ (avol[m0].mapped? → avol[m0].mapped? ∧ m0 < # avol) ⊦ n = 0, m0 < # avol ∧ avol[m0].mapped? ∧ # avol[m0].data ≤ m ∧ is-aligned(m, EB_PAGE_SIZE) ∧ is-aligned(n0, EB_PAGE_SIZE) ∧ m + n0 ≤ LEB_SIZE ∧ n1 + n0 ≤ # buf

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 62:
LEB_SIZE = (n4 + n) + m1, avols[default-volid][m2] = mapped(buf0, n2), m2 < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), default-volid ∈ avols, n + m1 ≤ LEB_SIZE, n3 + n ≤ # buf, m1 + n ≤ LEB_SIZE, n2 ≤ m1, m1 ≤ LEB_SIZE, n2 ≤ LEB_SIZE ⊦ n = 0, ∃ buf, n. mapped(buf0, n2) = mapped(buf, n)

Rule argument

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ abs(mapped(buf, n)) = mapped(subarray(buf, 0, n)); (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ abs(leb).mapped? ↔ (∃ buf, n. leb = mapped(buf, n)); (s)% ⊦ n < # evol → abs(evol)[n] = abs(evol[n]); (s)% ⊦ # abs(evol) = # evol; (s)