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Proof step 26 from proof abs-nodes-no-padding-last (previous step)

# buf1 = a0.alignedsize + 2 * NODE_HEADER_SIZE, # buf0 = (x0 + a ').flashsize, abs-node(buf1, a0), abs-nodes(buf0, m0 + # buf1, x0 + a ', lax1 + ladr ', false), ∃ buf3, buf. buf0 = buf3 + buf ∧ abs-nodes(buf3, m0 + # buf1, x0, lax1, false) ∧ abs-node(buf, a) ∧ ladr = @(# buf3 + m0 + # buf1, 2 * NODE_HEADER_SIZE + a.alignedsize), ∀ 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)) ⊦ ∃ buf, buf2. buf1 + buf0 = buf + buf2 ∧ abs-nodes(buf, m0, a0 ' + x0, @(m0, # buf1) ' + lax1, false) ∧ abs-node(buf2, a) ∧ ladr = @(# buf + m0, 2 * NODE_HEADER_SIZE + a.alignedsize)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
# buf = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf1 = a0.alignedsize + 2 * NODE_HEADER_SIZE, # buf2 + # buf = (x0 + a ').flashsize, abs-node(buf1, a0), abs-node(buf, a), abs-nodes(buf2 + buf, m0 + # buf1, x0 + a ', lax1 + @(# buf2 + m0 + # buf1, # buf) ', false), abs-nodes(buf2, m0 + # buf1, x0, lax1, false), ∀ buf3, x, a, m, lax, ladr. # buf3 < #(buf1 + buf2 + buf) → # buf3 = (x + a ').flashsize ∧ abs-nodes(buf3, m, x + a ', lax + ladr ', false) → (∃ buf4, buf1. buf3 = buf4 + buf1 ∧ abs-nodes(buf4, m, x, lax, false) ∧ abs-node(buf1, a) ∧ ladr = @(# buf4 + m, 2 * NODE_HEADER_SIZE + a.alignedsize)) ⊦ ∃ buf4, buf3. buf1 + buf2 + buf = buf4 + buf3 ∧ abs-nodes(buf4, m0, a0 ' + x0, @(m0, # buf1) ' + lax1, false) ∧ abs-node(buf3, a) ∧ @(# buf2 + m0 + # buf1, # buf) = @(# buf4 + m0, # buf)

Rule argument

Additional information

Used simplifier rules: ls-abs-node-buf-size: ⊦ abs-node(buf, nd) → # buf = nd.alignedsize + 2 * NODE_HEADER_SIZE;%c: ⊦ m + n = n + m; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)