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Proof step 25 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf0 = NODE_HEADER_SIZE, # buf = a.alignedsize, buf0 + subarray(buf + validtrailer, 0, n0) = buf2 + buf1, n0 < NODE_HEADER_SIZE + a.alignedsize, abs-nodes(buf1, m + # buf2, a ', @(m, 2 * NODE_HEADER_SIZE + a.alignedsize) ', boolvar), abs-padding(buf2), is-aligned(n0, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-encoded(a, subarray(buf, 0, node-size-headerless(a))), is-encoded(nodeheader(node-size-headerless(a), false), buf0), ∀ buf, buf1, a, n, m, x, lax, boolvar. # buf < # mkbuf(0) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf + buf1, 0, n), m, x + a ', lax + @(m + # buf, # buf1) ', boolvar) ∧ abs-nodes(buf, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf + # buf1 ⊦ NODE_HEADER_SIZE + a.alignedsize = n0, buf0 + buf + validtrailer = mkbuf(0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ abs-padding(buf) ↔ (∃ buf0, buf1. buf = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(# buf1, true), buf0) ∧ is-aligned(# buf1, 2 * NODE_HEADER_SIZE))
Proof step 27:
# buf = a.alignedsize, # buf0 = NODE_HEADER_SIZE, buf0 + subarray(buf + validtrailer, 0, n0) = buf2 + buf1, n0 < NODE_HEADER_SIZE + a.alignedsize, abs-nodes(buf1, m + # buf2, a ', @(m, 2 * NODE_HEADER_SIZE + a.alignedsize) ', boolvar), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n0, NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(a), false), buf0), is-encoded(a, subarray(buf, 0, node-size-headerless(a))), ∃ buf0, buf1. buf2 = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(# buf1, true), buf0) ∧ is-aligned(# buf1, 2 * NODE_HEADER_SIZE), ∀ buf, buf1, a, n, m, x, lax, boolvar. # buf < # mkbuf(0) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf + buf1, 0, n), m, x + a ', lax + @(m + # buf, # buf1) ', boolvar) ∧ abs-nodes(buf, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf + # buf1 ⊦ buf0 + buf + validtrailer = mkbuf(0), NODE_HEADER_SIZE + a.alignedsize = n0

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] → [buf2] flags: <all paths>

Additional information

Used terms: buf2