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Proof step 24 from proof abs-nodes-add-crash-aligned (previous step)

# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, abs-nodes(buf0, 0, x, lax, false), is-aligned(# buf0 + # buf1, EB_PAGE_SIZE), ∃ buf0, buf2. buf1 = buf0 + buf2 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(a), false), buf0) ∧ is-encoded(a, subarray(buf2, 0, node-size-headerless(a))) ∧ # buf2 = a.alignedsize ⊦ ∃ buf, buf2. buf1 = buf + buf2 ∧ ( abs-padding(buf) ∧ abs-nodes(buf2, # buf0 + # buf, a ', @(# buf0, # buf + # buf2) ', boolvar) ∨ buf2 = mkbuf(0) ∧ abs-node(buf, a))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# buf = a.alignedsize, # buf2 = NODE_HEADER_SIZE, abs-nodes(buf0, 0, x, lax, false), is-aligned(2 * NODE_HEADER_SIZE + # buf0 + a.alignedsize, EB_PAGE_SIZE), is-encoded(nodeheader(node-size-headerless(a), false), buf2), is-encoded(a, subarray(buf, 0, node-size-headerless(a))) ⊦ ∃ buf4, buf3. buf2 + buf + validtrailer = buf4 + buf3 ∧ ( abs-padding(buf4) ∧ abs-nodes(buf3, # buf0 + # buf4, a ', @(# buf0, # buf4 + # buf3) ', boolvar) ∨ buf3 = mkbuf(0) ∧ abs-node(buf4, a))

Rule argument

Additional information

Used simplifier rules: ⊦ m + m = 2 * m; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%lfw-is-encoded-nodeheader-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification abs-node%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m0 * 1 = m0; (s)%m2 ≠ 0 ⊦ (* m2) * m + n = m + n0 ↔ (m2 - 1) * m + n = n0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)