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Proof step 172 from proof refine-write (previous step)

avols[default-volid][m2] = mapped(buf0, n4), avol = abs(avols[default-volid]), m = m1, m0 = m2, n0 = n, n1 = n3, m0 < # avol, m2 < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), default-volid ∈ avols, n4 ≤ m1, m1 + n ≤ LEB_SIZE, n3 + n ≤ # buf, ⌊err0⌋ ⊦ n = 0, m0 < # avol ∧ (avol[m0].mapped? → avol[m0].mapped? ∧ m0 < # avol)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 173:
avols[default-volid][m2] = mapped(buf0, n4), 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, n3 + n ≤ # buf, m1 + n ≤ LEB_SIZE, n4 ≤ m1, ⌊err0⌋ ⊦ n = 0, ∃ buf, n. mapped(buf0, n4) = mapped(buf, n)

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf, m) = mapped(buf0, m0) ↔ buf = buf0 ∧ m = m0; (ws)% ⊦ abs(leb).mapped? ↔ (∃ buf, n. leb = mapped(buf, n)); (s)% ⊦ n < # evol → abs(evol)[n] = abs(evol[n]); (s)% ⊦ # abs(evol) = # evol; (s)