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Proof step 7 from proof abs-padding-abs-failed-append (previous step)

# buf3 = NODE_HEADER_SIZE, # buf = NODE_HEADER_SIZE, buf + (buf2 + validtrailer) + buf1 = buf3 + buf4, is-aligned(# buf1, NODE_HEADER_SIZE), is-aligned(# buf2, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf2, true), buf), is-garbage-header(buf3) ∨ is-encoded(nodeheader(m, boolvar), buf3) ∧ # buf4 ≤ align↑(m, 2 * NODE_HEADER_SIZE) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: append-inj seq: ⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2) subst: [buf2, buf0, buf1, buf] → [buf4, buf3, (buf2 + validtrailer) + buf1, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ is-encoded(ndhd, buf) → ¬ is-garbage-header(buf); (s)% ⊦ is-encoded(ndhd, buf) → (is-encoded(ndhd0, buf) ↔ ndhd = ndhd0); (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%⊦ nodeheader(m, boolvar) = nodeheader(m0, boolvar0) ↔ m = m0 ∧ (boolvar ↔ boolvar0); (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%m ≠ 0 ⊦ is-aligned(n, m) → n % m = 0; (s)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)%is-encoded-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification encoding-fixed-size-nonempty[encoding-node-header]% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: buf4, buf3, (buf2 + validtrailer) + buf1, buf