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Proof step 38 from proof abs-nodes-prefix-h (previous step)

# buf2 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf2, nd), abs-nodes(buf + buf1, m + # buf2, x2, lax3, boolvar1), abs-nodes(buf, m + # buf2, x, lax2, boolvar0), ∀ buf3, buf1, m, x1, lax1, boolvar1, x0, lax0, boolvar0. # buf3 < #(buf2 + buf) → abs-nodes(buf3 + buf1, m, x1, lax1, boolvar1) ∧ abs-nodes(buf3, m, x0, lax0, boolvar0) → x0 ⊑ x1 ∧ lax0 ⊑ lax1 ⊦ x ⊑ x2 ∧ lax2 ⊑ lax3

User applied rule apply induction

And closed the goal!

Rule argument

subst: [buf3, buf1, m, x1, lax1, boolvar1, x0, lax0, boolvar0] → [buf, buf1, m + nd.alignedsize + 2 * NODE_HEADER_SIZE, x2, lax3, boolvar1, x, lax2, boolvar0]

Additional information

Used simplifier rules: ⊦ #(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)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # mkbuf(n) = n; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)% ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ NODE_HEADER_SIZE ≠ 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, m + nd.alignedsize + 2 * NODE_HEADER_SIZE, x2, lax3, boolvar1, x, lax2, boolvar0