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Proof step 66 from proof abs-nodes-crash-h (previous step)

x = nd + x1, abs-nodes(buf, m, x, lax, true), is-aligned(n, NODE_HEADER_SIZE), n ≤ # buf, ∀ buf0, m, x, lax, n. # buf0 < # buf → abs-nodes(buf0, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf0 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf0, 0, n), m, x0, lax0, true)) ⊦ ∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf, 0, n), m, x0, lax0, true)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 67:
abs-nodes(buf, m, nd ' + x1, lax, true), is-aligned(n, NODE_HEADER_SIZE), n ≤ # buf, ∀ buf0, m, x, lax, n. # buf0 < # buf → abs-nodes(buf0, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf0 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf0, 0, n), m, x0, lax0, true)) ⊦ ∃ x, lax0. x ⊑ nd ' + x1 ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf, 0, n), m, x, lax0, true)

Rule argument

Additional information

Used simplifier rules: ⊦ a + x = a ' + x; (s)