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Proof step 45 from proof refine-write (previous step)

LEB_SIZE = (n4 + n) + n0 + n2, avols[default-volid][m2] = mapped(buf0, n2), m2 < # avols[default-volid], m2 < # avols[default-volid][m2, mapped(subarray(buf0, 0, n0 + n2) + subarray(buf, n3, n) + mkempbuf(n4), (n0 + n2) + n)], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), default-volid ∈ avols, (n0 + n2) + n ≤ LEB_SIZE, n3 + n ≤ # buf, n2 ≤ LEB_SIZE, n0 + n2 ≤ LEB_SIZE, n + n0 + n2 ≤ LEB_SIZE ⊦ mapped(subarray(buf0, 0, n2) + mkempbuf(n0) + subarray(buf, n3, n)) = abs(avols[default-volid][m2, mapped(subarray(buf0, 0, n0 + n2) + subarray(buf, n3, n) + mkempbuf(n4), (n0 + n2) + n)][m2]), n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
LEB_SIZE = (n4 + n) + n0 + n2, 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(n0, EB_PAGE_SIZE), default-volid ∈ avols, n + n0 + n2 ≤ LEB_SIZE, n0 + n2 ≤ LEB_SIZE, n2 ≤ LEB_SIZE, n3 + n ≤ # buf, (n0 + n2) + n ≤ LEB_SIZE ⊦ subarray(buf0, 0, n2) + mkempbuf(n0) = subarray(buf0, 0, n0 + n2), n = 0

Rule argument

Additional information

Used simplifier rules: ⊦ # evol[n, leb] = # evol; (s)% ⊦ buf + buf0 = buf1 + buf0 ↔ buf = buf1; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ abs(mapped(buf, n)) = mapped(subarray(buf, 0, n)); (s)% ⊦ m < # evol → evol[m, leb][m] = leb; (s)