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Proof step 15 from proof abs-nodes-crash-h (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ abs-padding(buf) ↔ (∃ buf0, buf1. buf = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(# buf1, true), buf0) ∧ is-aligned(# buf1, 2 * NODE_HEADER_SIZE))
Proof step 17:
n < # buf0, abs-nodes(buf1, m + # buf0, [], [], true), is-aligned(n, NODE_HEADER_SIZE), n ≤ # buf0 + # buf1, ∃ buf2, buf1. buf0 = buf2 + buf1 + validtrailer ∧ is-encoded(nodeheader(# buf1, true), buf2) ∧ is-aligned(# buf1, 2 * NODE_HEADER_SIZE), ∀ 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)) ⊦ buf0 = mkbuf(0), abs-nodes(subarray(buf0, 0, n), m, [], [], true)

Rule argument

spec: abs-node name: abs-padding seq: ⊦ abs-padding(buf) ↔ (∃ buf0, buf1. buf = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(# buf1, true), buf0) ∧ is-aligned(# buf1, 2 * NODE_HEADER_SIZE)) subst: [buf] → [buf0] flags: <all paths>

Additional information

Used terms: buf0