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Proof step 138 from proof refine-write (previous step)

LEB_SIZE = (n5 + n0) + n1 + n4, avols[default-volid][m2] = mapped(buf0, n4), n0 < n, m2 < # avols[default-volid], n2 < LEB_SIZE, n2 < n4 + n1, n4 < LEB_SIZE, ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(n1, EB_PAGE_SIZE), default-volid ∈ avols, n0 + n1 + n4 ≤ LEB_SIZE, n3 + n0 ≤ # buf, n1 + n4 ≤ LEB_SIZE, n3 + n ≤ # buf, (n1 + n4) + n ≤ LEB_SIZE, n4 ≤ n2, ⌊err1⌋ ⊦ n5 + n0 + n1 = 0, mkempbuf(n1)[n2 - n4] = buf0[n2], n0 = 0, n1 = 0

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n2, n4, n6]

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%⊦ m0 + m1 < LEB_SIZE ∧ v ∈ avols ∧ m < # avols[v] ∧ avols[v][m] = mapped(buf, m0) ∧ ebm-cons(avols) → buf[m1 + m0] = empty; (s)% ⊦ m ≤ m + n; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ m < n → mkempbuf(n)[m] = empty; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n2, n4, n6