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Proof step 172 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf3 = a0.alignedsize + 2 * NODE_HEADER_SIZE, n0 < # buf + # buf1, abs-node(buf3, a0), abs-node(buf1, a), abs-nodes(buf, m + # buf3, x0, lax0, false), abs-nodes(subarray(buf + buf1, 0, n0), m + # buf3, x0 + a ', lax0 + @(m + # buf3 + # buf, # buf1) ', boolvar), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n0, NODE_HEADER_SIZE), ∀ buf0, buf1, a, n, m, x, lax, boolvar. # buf0 < #(buf3 + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf0 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf0 + buf1, 0, n), m, x + a ', lax + @(m + # buf0, # buf1) ', boolvar) ∧ abs-nodes(buf0, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf0 + # buf1 ⊦ n0 = # buf + # buf1

User applied rule apply induction

And closed the goal!

Rule argument

subst: [buf0, buf1, a, n, m, x, lax, boolvar] → [buf, buf1, a, n0, m + # buf3, x0, lax0, boolvar]

Additional information

Used simplifier rules: abs-nodes-unique-strong-h: ⊦ abs-nodes(buf, m, x0, lax0, false) → (abs-nodes(buf, m, x1, lax1, boolvar1) ↔ x0 = x1 ∧ lax0 = lax1);% ⊦ abs-node(buf, nd0) → (abs-node(buf, nd1) ↔ nd0 = nd1); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ abs-node(buf, nd) → is-aligned(# buf, NODE_HEADER_SIZE); (ss)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ 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 Used terms: buf, buf1, a, n0, m + # buf3, x0, lax0, boolvar