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Proof step 34 from proof abs-nodes-crash-h (previous step)

abs-nodes(buf1, m + # buf0, [], [], true), abs-padding(buf0), is-aligned(n, NODE_HEADER_SIZE), # buf0 ≤ n, n ≤ # buf0 + # buf1, ∀ buf2, m, x, lax, n. # buf2 < #(buf0 + buf1) → abs-nodes(buf2, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf2 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf2, 0, n), m, x0, lax0, true)) ⊦ abs-nodes(buf0 + subarray(buf1, 0, n - # buf0), m, [], [], true)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
abs-nodes(buf1, m + # buf0, [], [], true), abs-padding(buf0), is-aligned(n, NODE_HEADER_SIZE), # buf0 ≤ n, n ≤ # buf0 + # buf1, ∀ buf2, m, x, lax, n. # buf2 < #(buf0 + buf1) → abs-nodes(buf2, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf2 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf2, 0, n), m, x0, lax0, true)) ⊦ abs-nodes(subarray(buf1, 0, n - # buf0), m + # buf0, [], [], true)

Rule argument

Additional information

Used simplifier rules: abs-nodes-padding-prefix: ⊦ abs-padding(buf0) → ( abs-nodes(buf0 + buf1, m, x, lax, weak) ↔ abs-nodes(buf1, m + # buf0, x, lax, weak));%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]