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Proof step 15 from proof abs-nodes-no-padding-last (previous step)

# buf = (2 * NODE_HEADER_SIZE + a0.alignedsize) + (x0 + a ').flashsize, # buf = (a0 ' + x0 + a ').flashsize, ∃ buf0, buf1. buf = buf0 + buf1 ∧ lax + ladr ' ≠ [] ∧ (lax + ladr ').head.off = m ∧ (lax + ladr ').head.size = # buf0 ∧ abs-node(buf0, a0) ∧ abs-nodes(buf1, m + # buf0, x0 + a ', (lax + ladr ').tail, false), ∀ buf0, x, a, m, lax, ladr. # buf0 < # buf → # buf0 = (x + a ').flashsize ∧ abs-nodes(buf0, m, x + a ', lax + ladr ', false) → (∃ buf2, buf1. buf0 = buf2 + buf1 ∧ abs-nodes(buf2, m, x, lax, false) ∧ abs-node(buf1, a) ∧ ladr = @(# buf2 + m, 2 * NODE_HEADER_SIZE + a.alignedsize)) ⊦ ∃ buf0, buf1. buf = buf0 + buf1 ∧ abs-nodes(buf0, m, a0 ' + x0, lax, false) ∧ abs-node(buf1, a) ∧ ladr = @(# buf0 + m, 2 * NODE_HEADER_SIZE + a.alignedsize)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
# buf1 = a0.alignedsize + 2 * NODE_HEADER_SIZE, # buf0 = (x0 + a ').flashsize, (lax + ladr ').head.size = # buf1, abs-node(buf1, a0), abs-nodes(buf0, (lax + ladr ').head.off + # buf1, x0 + a ', (lax + ladr ').tail, false), ∀ buf2, x, a, m, lax, ladr. # buf2 < #(buf1 + buf0) → # buf2 = (x + a ').flashsize ∧ abs-nodes(buf2, m, x + a ', lax + ladr ', false) → (∃ buf3, buf1. buf2 = buf3 + buf1 ∧ abs-nodes(buf3, m, x, lax, false) ∧ abs-node(buf1, a) ∧ ladr = @(# buf3 + m, 2 * NODE_HEADER_SIZE + a.alignedsize)) ⊦ ∃ buf3, buf2. buf1 + buf0 = buf3 + buf2 ∧ abs-nodes(buf3, (lax + ladr ').head.off, a0 ' + x0, lax, false) ∧ abs-node(buf2, a) ∧ ladr = @(# buf3 + (lax + ladr ').head.off, 2 * NODE_HEADER_SIZE + a.alignedsize)

Rule argument

Additional information

Used simplifier rules: size-rec: ⊦ (a ' + x).flashsize = a.flashsize + x.flashsize;%ls-abs-node-buf-size: ⊦ abs-node(buf, nd) → # buf = nd.alignedsize + 2 * NODE_HEADER_SIZE;% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ lax + ladr ' ≠ []; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ nd.flashsize = 2 * NODE_HEADER_SIZE + nd.alignedsize; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)