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Proof step 52 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf5 = NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, subarray(buf5 + buf4 + validtrailer, 0, n) = buf3 + buf0, n < 2 * NODE_HEADER_SIZE + # buf4 + # buf2 + # buf1, n < 2 * NODE_HEADER_SIZE + # buf4, abs-node(buf1, a), abs-nodes(buf0, m + # buf3, a ', @(2 * NODE_HEADER_SIZE + m + # buf4 + # buf2, # buf1) ', boolvar), abs-nodes(buf2, 2 * NODE_HEADER_SIZE + m + # buf4, [], [], false), abs-padding(buf3), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-aligned(# buf4, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf4, true), buf5), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #((buf5 + buf4 + validtrailer) + buf2) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf3 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf3 + buf1, 0, n), m, x + a ', lax + @(m + # buf3, # buf1) ', boolvar) ∧ abs-nodes(buf3, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf3 + # buf1 ⊦ buf5 + buf4 + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + # buf4 + # buf2 + # buf1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 53:
⊦ abs-padding(buf) ↔ (∃ buf0, buf1. buf = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(# buf1, true), buf0) ∧ is-aligned(# buf1, 2 * NODE_HEADER_SIZE))
Proof step 54:
# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf5 = NODE_HEADER_SIZE, subarray(buf5 + buf4 + validtrailer, 0, n) = buf3 + buf0, n < 2 * NODE_HEADER_SIZE + # buf4, n < 2 * NODE_HEADER_SIZE + # buf4 + # buf2 + # buf1, abs-node(buf1, a), abs-nodes(buf2, 2 * NODE_HEADER_SIZE + m + # buf4, [], [], false), abs-nodes(buf0, m + # buf3, a ', @(2 * NODE_HEADER_SIZE + m + # buf4 + # buf2, # buf1) ', boolvar), is-aligned(# buf4, 2 * NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), is-encoded(nodeheader(# buf4, true), buf5), ∃ buf0, buf1. buf3 = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(# buf1, true), buf0) ∧ is-aligned(# buf1, 2 * NODE_HEADER_SIZE), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #((buf5 + buf4 + validtrailer) + buf2) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf3 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf3 + buf1, 0, n), m, x + a ', lax + @(m + # buf3, # buf1) ', boolvar) ∧ abs-nodes(buf3, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf3 + # buf1 ⊦ buf5 + buf4 + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + # buf4 + # buf2 + # buf1

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] → [buf3] flags: <all paths>

Additional information

Used terms: buf3