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Proof step 7 from proof abs-nodes-no-padding-last (previous step)

# buf = (x + a ').flashsize, x = [], abs-nodes(buf, m, x + a ', lax + ladr ', 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, x, 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 8:
# buf = 2 * NODE_HEADER_SIZE + a.alignedsize, abs-nodes(buf, m, a ', lax + ladr ', 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, [], lax, false) ∧ abs-node(buf1, a) ∧ ladr = @(# buf0 + m, # buf0 + # buf1)

Rule argument

Additional information

Used simplifier rules: flashsize-one: ⊦ a '.flashsize = a.flashsize;%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ nd.flashsize = 2 * NODE_HEADER_SIZE + nd.alignedsize; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ [] + x = x; (s)