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Proof step 70 from proof abs-nodes-crash-h (previous step)

is-aligned(n, NODE_HEADER_SIZE), n ≤ # buf1 + # buf0, abs-padding(buf1) ∧ abs-nodes(buf0, m + # buf1, nd ' + x1, lax, true) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf1 ∧ abs-node(buf1, nd) ∧ abs-nodes(buf0, lax.head.off + # buf1, x1, lax.tail, true), ∀ buf2, m, x, lax, n. # buf2 < #(buf1 + buf0) → 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)) ⊦ ∃ x, lax0. x ⊑ nd ' + x1 ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf1 + buf0, 0, n), m, x, lax0, true)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 71:
lax.head = @(m0, m1), is-aligned(n, NODE_HEADER_SIZE), n ≤ # buf1 + # buf0, abs-padding(buf1) ∧ abs-nodes(buf0, m + # buf1, nd ' + x1, lax, true) ∨ lax ≠ [] ∧ m0 = m ∧ m1 = # buf1 ∧ abs-node(buf1, nd) ∧ abs-nodes(buf0, m0 + # buf1, x1, lax.tail, true), ∀ buf2, m, x, lax, n. # buf2 < #(buf1 + buf0) → 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)) ⊦ ∃ x, lax0. x ⊑ nd ' + x1 ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf1 + buf0, 0, n), m, x, lax0, true)

Rule argument

spec: laddress name: elim seq: ⊦ m = ladr.off ∧ m0 = ladr.size ↔ ladr = @(m, m0) subst: [ladr, m, m0] → [lax.head, m0, m1]

Additional information

Used simplifier rules: ⊦ m = ladr.off ∧ m0 = ladr.size ↔ ladr = @(m, m0); (elim) Used terms: lax.head, m0, m1