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Proof step 5 from proof abs-nodes-crash-h (previous step)

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)

User applied rule constructor cut

And obtained the following new goals

Proof step 6:
x = [], 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)
Proof step 66:
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)

Rule argument

var: x

Additional information

Used simplifier rules: list freely generated by [], +;;