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

# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf1, nd), abs-nodes(buf2 + buf, m + # buf1, x + x1, lax0 + lax, weak), abs-nodes(buf, (m + # buf1) + # buf2, x1, lax, weak), abs-nodes(buf2, m + # buf1, x, lax0, false), ∀ buf3, m, x0, x1, lax, weak. # buf3 < #(buf1 + buf2 + buf) → abs-nodes(buf3, m, x0 + x1, lax, weak) → (∃ buf4, buf1, lax0, lax1. lax = lax0 + lax1 ∧ buf3 = buf4 + buf1 ∧ abs-nodes(buf4, m, x0, lax0, false) ∧ abs-nodes(buf1, m + # buf4, x1, lax1, weak)) ⊦ @(m, # buf1) ' + lax0 + lax = (@(m, nd.alignedsize + 2 * NODE_HEADER_SIZE) ' + lax0) + lax ∧ buf1 + buf2 + buf = (buf1 + buf2) + buf ∧ abs-nodes(buf1 + buf2, m, nd ' + x, @(m, nd.alignedsize + 2 * NODE_HEADER_SIZE) ' + lax0, false) ∧ abs-nodes(buf, m + #(buf1 + buf2), x1, lax, weak)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf1, nd), abs-nodes(buf2, m + # buf1, x, lax0, false), abs-nodes(buf, (m + # buf1) + # buf2, x1, lax, weak), abs-nodes(buf2 + buf, m + # buf1, x + x1, lax0 + lax, weak), ∀ buf3, m, x0, x1, lax, weak. # buf3 < #(buf1 + buf2 + buf) → abs-nodes(buf3, m, x0 + x1, lax, weak) → (∃ buf4, buf1, lax0, lax1. lax = lax0 + lax1 ∧ buf3 = buf4 + buf1 ∧ abs-nodes(buf4, m, x0, lax0, false) ∧ abs-nodes(buf1, m + # buf4, x1, lax1, weak)) ⊦ abs-nodes(buf1 + buf2, m, nd ' + x, @(m, # buf1) ' + lax0, false)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ @(m, m0) = @(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ ladr ' + lax = ladr0 ' + lax ↔ ladr = ladr0; (s)