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Proof step 74 from proof abs-nodes-crash-h (previous step)

abs-nodes(buf0, m + # buf1, nd ' + x1, @(m0, m1) ' + lax0, true), abs-padding(buf1), is-aligned(n, NODE_HEADER_SIZE), n ≤ # buf1 + # buf0, ∀ 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, lax1. x ⊑ nd ' + x1 ∧ lax1 ⊑ @(m0, m1) ' + lax0 ∧ abs-nodes(subarray(buf1 + buf0, 0, n), m, x, lax1, true)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 75:
⊦ abs-padding(buf) ↔ (∃ buf0, buf1. buf = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(# buf1, true), buf0) ∧ is-aligned(# buf1, 2 * NODE_HEADER_SIZE))
Proof step 76:
abs-nodes(buf0, m + # buf1, nd ' + x1, @(m0, m1) ' + lax0, true), is-aligned(n, NODE_HEADER_SIZE), n ≤ # buf1 + # buf0, ∃ buf0, buf2. buf1 = buf0 + buf2 + validtrailer ∧ is-encoded(nodeheader(# buf2, true), buf0) ∧ is-aligned(# buf2, 2 * NODE_HEADER_SIZE), ∀ 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, lax1. x ⊑ nd ' + x1 ∧ lax1 ⊑ @(m0, m1) ' + lax0 ∧ abs-nodes(subarray(buf1 + buf0, 0, n), m, x, lax1, 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] → [buf1] flags: <all paths>

Additional information

Used terms: buf1