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Proof step 18 from proof abs-nodes-beyond-no-address-h (previous step)

# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf1, nd), abs-nodes(buf0, m + # buf1, x0, lax0, boolvar), (# buf1 + # buf0) + m ≤ m0, @(m0, m1) = @(m, # buf1) ∨ @(m0, m1) ∈ lax0, ∀ buf2, m, x, lax, boolvar, m0, m1. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x, lax, boolvar) ∧ @(m0, m1) ∈ lax ∧ # buf2 + m ≤ m0 → false ⊦

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 5

Additional information

Used simplifier rules: abs-nodes-nospace-h: # buf < NODE_HEADER_SIZE ⊦ abs-nodes(buf, m, x, lax, boolvar) ↔ x = [] ∧ lax = [] ∧ buf = mkbuf(0);% ⊦ @(m, m0) = @(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # mkbuf(n) = n; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ 2 * m = 0 ↔ m = 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult