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Proof step 44 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, n < # buf, n < (# buf + # buf2) + # buf1, abs-node(buf1, a), abs-nodes(subarray(buf, 0, n), m, a ', @(m + # buf + # buf2, # buf1) ', boolvar), abs-nodes(buf2, m + # buf, [], [], false), abs-padding(buf), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf + 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 ⊦ buf = mkbuf(0), n = (# buf + # buf2) + # buf1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ abs-nodes(buf, m, a ', lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ', lax, weak) ∨ lax = @(m, a.flashsize) ' ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, [], [], weak)))
Proof step 46:
# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, n < (# buf + # buf2) + # buf1, n < # buf, abs-node(buf1, a), abs-nodes(buf2, m + # buf, [], [], false), abs-padding(buf), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), ∃ buf0, buf3. subarray(buf, 0, n) = buf0 + buf3 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf3, m + # buf0, a ', @(m + # buf + # buf2, # buf1) ', boolvar) ∨ @(m + # buf + # buf2, # buf1) ' = @(m, a.flashsize) ' ∧ abs-node(buf0, a) ∧ abs-nodes(buf3, m + # buf0, [], [], boolvar)), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf + 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 ⊦ buf = mkbuf(0), n = (# buf + # buf2) + # buf1

Rule argument

spec: <toplevel> name: abs-nodes-one-h seq: ⊦ abs-nodes(buf, m, a ', lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ', lax, weak) ∨ lax = @(m, a.flashsize) ' ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, [], [], weak))) subst: [weak, lax, a, m, buf] → [boolvar, @(m + # buf + # buf2, # buf1) ', a, m, subarray(buf, 0, n)] flags: <all paths>

Additional information

Used terms: boolvar, @(m + # buf + # buf2, # buf1) ', a, m, subarray(buf, 0, n)