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Proof step 18 from proof abs-nodes-no-padding-last (previous step)

# buf0 = (x0 + a ').flashsize, # buf1 = a0.alignedsize + 2 * NODE_HEADER_SIZE, lax + ladr ' = ladr0 ' + lax0, ladr0.size = # buf1, abs-node(buf1, a0), abs-nodes(buf0, ladr0.off + # buf1, x0 + a ', lax0, false), ladr = ladr0 ∨ ladr ∈ lax0, ladr0 ∈ lax ∨ ladr0 = ladr, ∀ 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, ladr0.off, a0 ' + x0, lax, false) ∧ abs-node(buf2, a) ∧ ladr = @(# buf3 + ladr0.off, 2 * NODE_HEADER_SIZE + a.alignedsize)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
# buf1 = a0.alignedsize + 2 * NODE_HEADER_SIZE, # buf0 = (x0 + a ').flashsize, lax + ladr ' = ladr0 ' + lax0, ladr0 = @(m0, m1), m1 = # buf1, abs-node(buf1, a0), abs-nodes(buf0, m0 + # buf1, x0 + a ', lax0, false), ladr0 ∈ lax ∨ ladr0 = ladr, ladr = ladr0 ∨ ladr ∈ lax0, ∀ 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, m0, a0 ' + x0, lax, false) ∧ abs-node(buf2, a) ∧ ladr = @(# buf3 + m0, 2 * NODE_HEADER_SIZE + a.alignedsize)

Rule argument

spec: laddress name: elim seq: ⊦ m = ladr.off ∧ m0 = ladr.size ↔ ladr = @(m, m0) subst: [ladr, m, m0] → [ladr0, m0, m1]

Additional information

Used simplifier rules: ⊦ m = ladr.off ∧ m0 = ladr.size ↔ ladr = @(m, m0); (elim) Used terms: ladr0, m0, m1