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Proof step 10 from proof abs-nodes-crash-h (previous step)

is-aligned(n, NODE_HEADER_SIZE), n ≤ # buf, buf = mkbuf(0) ∨ buf = buf0 + buf1 ∧ abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, [], [], true) ∨ abs-failed(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)) ⊦ abs-nodes(subarray(buf, 0, n), m, [], [], true)

User applied rule case distinction

And obtained the following new goals

Proof step 11:
buf = buf0 + buf1, abs-nodes(buf1, m + # buf0, [], [], true), abs-padding(buf0), 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)) ⊦ abs-nodes(subarray(buf, 0, n), m, [], [], true)
Proof step 44:
abs-failed(buf), 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)) ⊦ abs-nodes(subarray(buf, 0, n), m, [], [], true)

Rule argument

pos: left 3

Additional information

Used simplifier rules: abs-nodes-mkbuf0-empty-h: ⊦ abs-nodes(mkbuf(0), m, x, lax, weak) ↔ x = [] ∧ lax = [];% ⊦ # mkbuf(n) = n; (s)% ⊦ m ≤ 0 ↔ m = 0; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)