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Proof step 39 from proof abs-nodes-crash-h (previous step)

abs-nodes(buf1, m + # buf0, [], [], true), abs-padding(buf0), is-aligned(n0 + # buf0, NODE_HEADER_SIZE), n0 ≤ # 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, n0), m + # buf0, [], [], true), is-aligned(n0, NODE_HEADER_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 40:
m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m)
Proof step 41:
abs-nodes(buf1, m + # buf0, [], [], true), abs-padding(buf0), is-aligned(n0 + # buf0, NODE_HEADER_SIZE), n0 ≤ # 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, n0), m + # buf0, [], [], true), is-aligned(n0, NODE_HEADER_SIZE), NODE_HEADER_SIZE ≠ 0 ∧ is-aligned(# buf0, NODE_HEADER_SIZE)

Rule argument

spec: align name: is-aligned-add seq: m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m) subst: [m, n1, n0] → [NODE_HEADER_SIZE, # buf0, n0] flags: <all paths>

Additional information

Used terms: NODE_HEADER_SIZE, # buf0, n0