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Proof step 103 from proof abs-nodes-crash-h (previous step)

# buf2 = NODE_HEADER_SIZE, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + # buf, nd ' + x1, @(m0, m1) ' + lax0, true), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-aligned(n0, NODE_HEADER_SIZE), is-encoded(nodeheader(# buf, true), buf2), n0 ≤ # buf0, ∀ buf3, m, x, lax, n. # buf3 < #((buf2 + buf + validtrailer) + buf0) → abs-nodes(buf3, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf3 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf3, 0, n), m, x0, lax0, true)) ⊦ ∃ x, lax. x ⊑ nd ' + x1 ∧ lax ⊑ @(m0, m1) ' + lax0 ∧ abs-nodes(buf2 + buf + validtrailer + subarray(buf0, 0, n0), m, x, lax, true)

User applied rule apply induction

And obtained the following new goals

Proof step 104:
# buf2 = NODE_HEADER_SIZE, abs-nodes(buf0, 2 * NODE_HEADER_SIZE + m + # buf, nd ' + x1, @(m0, m1) ' + lax0, true), is-aligned(n0, NODE_HEADER_SIZE), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf, true), buf2), n0 ≤ # buf0, ∃ x0, lax1. x0 ⊑ nd ' + x1 ∧ lax1 ⊑ @(m0, m1) ' + lax0 ∧ abs-nodes(subarray(buf0, 0, n0), 2 * NODE_HEADER_SIZE + m + # buf, x0, lax1, true), ∀ buf3, m, x, lax, n. # buf3 < #((buf2 + buf + validtrailer) + buf0) → abs-nodes(buf3, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf3 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf3, 0, n), m, x0, lax0, true)) ⊦ ∃ x, lax. x ⊑ nd ' + x1 ∧ lax ⊑ @(m0, m1) ' + lax0 ∧ abs-nodes(buf2 + buf + validtrailer + subarray(buf0, 0, n0), m, x, lax, true)

Rule argument

subst: [buf3, m, x, lax, n] → [buf0, 2 * NODE_HEADER_SIZE + m + # buf, nd ' + x1, @(m0, m1) ' + lax0, n0]

Additional information

Used simplifier rules: abs-nodes-unique-weak-h: ⊦ abs-nodes(buf, m, x0, lax0, true) → (abs-nodes(buf, m, x1, lax1, true) ↔ x0 = x1 ∧ lax0 = lax1);%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (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)% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s) Used terms: buf0, 2 * NODE_HEADER_SIZE + m + # buf, nd ' + x1, @(m0, m1) ' + lax0, n0