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Proof step 3 from proof abs-nodes-crash (previous step)

abs-nodes(buf, 0, x, lax, true) ⊦ ∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(buf.align↓, 0, x0, lax0, true)

User applied rule apply lemma

And obtained the following new goals

Proof step 4:
⊦ abs-nodes(buf, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf, 0, n), m, x0, lax0, true))
Proof step 5:
abs-nodes(buf, 0, x, lax, true), abs-nodes(buf, 0, x, lax, true) ∧ is-aligned(# buf.align↓, NODE_HEADER_SIZE) ∧ # buf.align↓ ≤ # buf → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf, 0, # buf.align↓), 0, x0, lax0, true)) ⊦ ∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(buf.align↓, 0, x0, lax0, true)

Rule argument

spec: <toplevel> name: abs-nodes-crash-h seq: ⊦ abs-nodes(buf, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf, 0, n), m, x0, lax0, true)) subst: [buf, m, x, lax, n] → [buf, 0, x, lax, # buf.align↓]

Additional information

Used terms: buf, 0, x, lax, # buf.align↓