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Proof step 50 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf5 = NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, subarray(buf5 + buf4 + validtrailer, 0, n) = buf3 + buf0, n < 2 * NODE_HEADER_SIZE + # buf4 + # buf2 + # buf1, n < 2 * NODE_HEADER_SIZE + # buf4, abs-node(buf1, a), abs-nodes(buf2, 2 * NODE_HEADER_SIZE + m + # buf4, [], [], false), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-aligned(# buf4, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf4, true), buf5), abs-padding(buf3) ∧ abs-nodes(buf0, m + # buf3, a ', @(2 * NODE_HEADER_SIZE + m + # buf4 + # buf2, # buf1) ', boolvar) ∨ @(2 * NODE_HEADER_SIZE + m + # buf4 + # buf2, # buf1) = @(m, # buf1) ∧ abs-node(buf3, a) ∧ abs-nodes(buf0, m + # buf3, [], [], boolvar), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #((buf5 + buf4 + validtrailer) + buf2) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf3 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf3 + buf1, 0, n), m, x + a ', lax + @(m + # buf3, # buf1) ', boolvar) ∧ abs-nodes(buf3, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf3 + # buf1 ⊦ buf5 + buf4 + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + # buf4 + # buf2 + # buf1

User applied rule case distinction

And obtained the following new goals

Proof step 51:
# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf5 = NODE_HEADER_SIZE, subarray(buf5 + buf4 + validtrailer, 0, n) = buf3 + buf0, n < 2 * NODE_HEADER_SIZE + # buf4, n < 2 * NODE_HEADER_SIZE + # buf4 + # buf2 + # buf1, abs-node(buf1, a), abs-nodes(buf2, 2 * NODE_HEADER_SIZE + m + # buf4, [], [], false), abs-nodes(buf0, m + # buf3, a ', @(2 * NODE_HEADER_SIZE + m + # buf4 + # buf2, # buf1) ', boolvar), abs-padding(buf3), is-aligned(# buf4, 2 * NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), is-encoded(nodeheader(# buf4, true), buf5), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #((buf5 + buf4 + validtrailer) + buf2) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf3 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf3 + buf1, 0, n), m, x + a ', lax + @(m + # buf3, # buf1) ', boolvar) ∧ abs-nodes(buf3, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf3 + # buf1 ⊦ buf5 + buf4 + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + # buf4 + # buf2 + # buf1

Rule argument

pos: left 12

Additional information

Used simplifier rules: ⊦ @(m, m0) = @(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ m = m + n ↔ n = 0; (s)% ⊦ 2 * NODE_HEADER_SIZE + n ≠ 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]