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Proof step 10 from proof abs-nodes-no-padding-last (previous step)

# buf = 2 * NODE_HEADER_SIZE + a.alignedsize, # buf = a '.flashsize, lax + ladr ' = @(m, # buf) ', abs-node(buf, a), ∀ 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, [], lax, false) ∧ abs-node(buf1, a) ∧ ladr = @(# buf0 + m, # buf0 + # buf1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
# buf = 2 * NODE_HEADER_SIZE + a.alignedsize, abs-node(buf, a), ∀ 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, [], [], false) ∧ abs-node(buf1, a) ∧ @(m, # buf0 + # buf1) = @(# buf0 + m, # buf0 + # buf1)

Rule argument

Additional information

Used simplifier rules: flashsize-one: ⊦ a '.flashsize = a.flashsize;%ls-abs-node-buf-size: ⊦ abs-node(buf, nd) → # buf = nd.alignedsize + 2 * NODE_HEADER_SIZE;%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ nd.flashsize = 2 * NODE_HEADER_SIZE + nd.alignedsize; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ ladr ' = lax + ladr0 ' ↔ ladr = ladr0 ∧ lax = []; (ws)