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Proof step 97 from proof refine-write (previous step)

LEB_SIZE - m1 = n0 + n2, avols[default-volid][m2] = mapped(buf0, n4), avol = abs(avols[default-volid]), n2 ≠ 0, n2 < n, 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), is-aligned(n2, EB_PAGE_SIZE), default-volid ∈ avols, n4 ≤ LEB_SIZE, m1 ≤ LEB_SIZE, n4 ≤ m1, m1 + n ≤ LEB_SIZE, n3 + n ≤ # buf, n3 + n2 ≤ # buf, n2 + m1 ≤ LEB_SIZE, ⌊err0⌋ ⊦ ⟨ebm_avol_write#(m2, m1, n3, n, buf; avol; err1)⟩ ( avol = abs(avols[default-volid][m2, mapped(subarray(avols[default-volid][m2].data, 0, m1) + subarray(buf, n3, n2) + mkempbuf(n0), m1 + n2)]) ∧ err0 = err1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 98:
LEB_SIZE = n1 + m1, avols[default-volid][m2] = mapped(buf0, n4), avol = abs(avols[default-volid]), n1 = n0 + n2, m2 < # avols[default-volid], n2 < n, ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n2, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), default-volid ∈ avols, n2 + m1 ≤ LEB_SIZE, n3 + n2 ≤ # buf, n3 + n ≤ # buf, m1 + n ≤ LEB_SIZE, n4 ≤ m1, m1 ≤ LEB_SIZE, n4 ≤ LEB_SIZE, ⌊err0⌋ ⊦ ⟨ebm_avol_write#(m2, m1, n3, n, buf; avol; err1)⟩ ( avol = abs(avols[default-volid][m2, mapped(subarray(avols[default-volid][m2].data, 0, m1) + subarray(buf, n3, n2) + mkempbuf(n0), m1 + n2)]) ∧ err0 = err1), n2 = 0

Rule argument

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

Additional information

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