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Proof step 119 from proof refine-write (previous step)

LEB_SIZE = (n5 + n0) + m1, avols[default-volid][m2] = mapped(buf0, n4), n0 < n, m2 < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), default-volid ∈ avols, n0 + m1 ≤ LEB_SIZE, n3 + n0 ≤ # buf, n4 ≤ m1, m1 ≤ LEB_SIZE, n4 ≤ LEB_SIZE, n3 + n ≤ # buf, m1 + n ≤ LEB_SIZE, ⌊err1⌋ ⊦ abs(avols[default-volid])[m2, mapped(subarray(buf0, 0, n4) + mkempbuf(m1 - n4) + subarray(buf, n3, n0))] = abs(avols[default-volid][m2, mapped(subarray(buf0, 0, m1) + subarray(buf, n3, n0) + mkempbuf(n5), m1 + n0)]), n0 = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 120:
LEB_SIZE = (n5 + n0) + m1, avols[default-volid][m2] = mapped(buf0, n4), m1 = n1 + n4, m2 < # avols[default-volid], n0 < n, ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(n0, EB_PAGE_SIZE), default-volid ∈ avols, m1 + n ≤ LEB_SIZE, n3 + n ≤ # buf, n4 ≤ LEB_SIZE, m1 ≤ LEB_SIZE, n4 ≤ m1, n3 + n0 ≤ # buf, n0 + m1 ≤ LEB_SIZE, ⌊err1⌋ ⊦ abs(avols[default-volid])[m2, mapped(subarray(buf0, 0, n4) + mkempbuf(n1) + subarray(buf, n3, n0))] = abs(avols[default-volid][m2, mapped(subarray(buf0, 0, m1) + subarray(buf, n3, n0) + mkempbuf(n5), m1 + n0)]), n0 = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [m1, n4, n1]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m1, n4, n1