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Proof step 4 from proof decode-node (previous step)

m = m1, m0 = n, m < 2 * NODE_HEADER_SIZE ⊦ ⟪debug#("persistence: decode_node expected size wrong"); err := EINVAL⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → (∃ buf0, buf1. subarray(buf, n, 2 * NODE_HEADER_SIZE + nd.alignedsize) = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) ∧ # buf1 = nd.alignedsize) ∧ m1 = 2 * NODE_HEADER_SIZE + nd.alignedsize ∧ n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
m1 < 2 * NODE_HEADER_SIZE ⊦ ⟪debug#("persistence: decode_node expected size wrong"); err := EINVAL⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → (∃ buf0, buf1. subarray(buf, n, 2 * NODE_HEADER_SIZE + nd.alignedsize) = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, buf1) ∧ # buf1 = nd.alignedsize) ∧ m1 = 2 * NODE_HEADER_SIZE + nd.alignedsize ∧ n + 2 * NODE_HEADER_SIZE + nd.alignedsize ≤ # buf))

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ 2 * m = 0 ↔ m = 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)