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Proof step 24 from proof abs-nodes-unique-weak-h (previous step)

# buf2 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf2, nd), abs-nodes(buf, (m + # buf0) + # buf2, x2, lax2, true), abs-nodes(buf2 + buf, m + # buf0, [], [], true), abs-padding(buf0), ∀ buf3, m, x0, lax0, x1, lax1. # buf3 < #(buf0 + buf2 + buf) → abs-nodes(buf3, m, x0, lax0, true) ∧ abs-nodes(buf3, m, x1, lax1, true) → x0 = x1 ∧ lax0 = lax1 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: abs-nodes-base seq: ⊦ abs-nodes(buf, m, [], lax, weak) ↔ # buf = 0 ∧ lax = [] ∨ (∃ buf0, buf1. buf = buf0 + buf1 ∧ abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, [], lax, weak)) ∨ weak ∧ abs-failed(buf) ∧ lax = [] subst: [weak, lax, m, buf] → [true, [], m + # buf0, buf2 + buf] flags: <all paths>

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);% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ abs-node(buf0, nd) ∧ buf0 + buf1 = buf + buf2 → ¬ abs-padding(buf); (s)% ⊦ abs-node(buf0, nd) → ¬ abs-failed(buf0 + buf1); (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 Used terms: true, [], m + # buf0, buf2 + buf