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Proof step 162 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, n0 < # buf + # buf1, abs-node(buf1, a), abs-nodes(subarray(buf + buf1, 0, n0), m + # buf2, (a0 ' + x0) + a ', (@(m0, m1) ' + lax0) + @(m + # buf2 + # buf, # buf1) ', boolvar), abs-nodes(buf, m + # buf2, a0 ' + x0, @(m0, m1) ' + lax0, false), abs-padding(buf2), is-aligned(n0 + # buf2, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf2 + buf) → # 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 ⊦ n0 = # buf + # buf1

User applied rule apply induction

And obtained the following new goals

Proof step 163:
# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, n0 < # buf + # buf1, abs-node(buf1, a), abs-nodes(buf, m + # buf2, a0 ' + x0, @(m0, m1) ' + lax0, false), abs-nodes(subarray(buf + buf1, 0, n0), m + # buf2, (a0 ' + x0) + a ', (@(m0, m1) ' + lax0) + @(m + # buf2 + # buf, # buf1) ', boolvar), abs-padding(buf2), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n0 + # buf2, NODE_HEADER_SIZE), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf2 + buf) → # 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 ⊦ n0 = # buf + # buf1, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n0 < # buf + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes (subarray(buf + buf1, 0, n0), m + # buf2, (a0 ' + x0) + a ', (@(m0, m1) ' + lax0) + @((m + # buf2) + # buf, # buf1) ', boolvar) ∧ abs-nodes(buf, m + # buf2, a0 ' + x0, @(m0, m1) ' + lax0, false) ∧ is-aligned(n0, NODE_HEADER_SIZE) ∧ is-aligned(m + # buf2, NODE_HEADER_SIZE)

Rule argument

subst: [buf3, buf1, a, n, m, x, lax, boolvar] → [buf, buf1, a, n0, m + # buf2, a0 ' + x0, @(m0, m1) ' + lax0, boolvar]

Additional information

Used simplifier rules: abs-nodes-unique-strong-h: ⊦ abs-nodes(buf, m, x0, lax0, false) → (abs-nodes(buf, m, x1, lax1, boolvar1) ↔ x0 = x1 ∧ lax0 = lax1);% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ # mkbuf(n) = n; (s)%n ≠ 0 ⊦ is-aligned(0, n); (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)% ⊦ n + 0 = n; (s)% ⊦ ¬ abs-padding(mkbuf(0)); (s)%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ a ' + x = a ' + y ↔ x = y; (s)% ⊦ x = x + y ↔ y = []; (s)% ⊦ a ' ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: buf, buf1, a, n0, m + # buf2, a0 ' + x0, @(m0, m1) ' + lax0, boolvar