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Proof step 20 from proof abs-nodes-nodups-h (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: abs-nodes-before-no-address-h seq: ⊦ abs-nodes(buf, m, x, lax, boolvar) ∧ m0 < m → ¬ @(m0, m1) ∈ lax subst: [buf, m, x, boolvar, lax, m1, m0] → [buf0, m + # buf1, x0, boolvar, lax0, # buf1, m] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < m + n ↔ n ≠ 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: buf0, m + # buf1, x0, boolvar, lax0, # buf1, m