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Proof step 23 from proof abs-nodes-prefix-h (previous step)

# buf2 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf2, nd), abs-nodes(buf, m + # buf2, x, lax2, boolvar0), # buf2 + # buf + # buf1 = 0 ∨ (buf2 + buf) + buf1 = buf0 + buf3 ∧ abs-padding(buf0) ∧ abs-nodes(buf3, m + # buf0, [], [], boolvar1), ∀ 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 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: abs-node name: abs-node-no-abs-padding seq: ⊦ abs-node(buf0, nd) ∧ buf0 + buf1 = buf + buf2 → ¬ abs-padding(buf) subst: [buf0, nd, buf1, buf2, buf] → [buf2, nd, buf + buf1, buf3, buf0] 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);%abs-nodes-nospace-h: # buf < NODE_HEADER_SIZE ⊦ abs-nodes(buf, m, x, lax, boolvar) ↔ x = [] ∧ lax = [] ∧ buf = mkbuf(0);% ⊦ 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% ⊦ abs-node(buf, nd0) → (abs-node(buf, nd1) ↔ nd0 = nd1); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer] Used terms: buf2, nd, buf + buf1, buf3, buf0