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Proof step 22 from proof abs-nodes-append-h (previous step)

lax0.head = @(m0, m1), (lax0 + lax1).head = @(m2, m3), abs-nodes(buf, m + # buf2, nd ' + x, lax0, false), abs-padding(buf2), ∀ buf3, m, x0, lax0, buf1, x1, lax1, weak. # buf3 < #(buf2 + buf) → abs-nodes(buf3, m, x0, lax0, false) → (abs-nodes(buf3 + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf3, x1, lax1, weak)) ⊦ (∃ buf0, buf3. (buf2 + buf) + buf1 = buf0 + buf3 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf3, m + # buf0, nd ' + x + x1, lax0 + lax1, weak) ∨ lax0 + lax1 ≠ [] ∧ m2 = m ∧ m3 = # buf0 ∧ abs-node(buf0, nd) ∧ abs-nodes(buf3, m + # buf0, x + x1, (lax0 + lax1).tail, weak))) ↔ abs-nodes(buf1, m + # buf2 + # buf, x1, lax1, weak)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
abs-nodes(buf, m + # buf2, nd ' + x, @(m2, m3) ' + lax, false), abs-padding(buf2), ∀ buf3, m, x0, lax0, buf1, x1, lax1, weak. # buf3 < #(buf2 + buf) → abs-nodes(buf3, m, x0, lax0, false) → (abs-nodes(buf3 + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf3, x1, lax1, weak)) ⊦ (∃ buf0, buf3. (buf2 + buf) + buf1 = buf0 + buf3 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf3, m + # buf0, nd ' + x + x1, (@(m2, m3) ' + lax) + lax1, weak) ∨ m2 = m ∧ m3 = # buf0 ∧ abs-node(buf0, nd) ∧ abs-nodes(buf3, m + # buf0, x + x1, lax + lax1, weak))) ↔ abs-nodes(buf1, m + # buf2 + # buf, x1, lax1, weak)

Rule argument

Additional information

Used simplifier rules: abs-nodes-first-adr-explicit: ⊦ abs-nodes(buf, m, a ' + x, lax, weak) → (lax.head = ladr ↔ (∃ lax0. lax = ladr + lax0));% ⊦ ladr ∈ ladr0 ' + lax ↔ ladr = ladr0 ∨ ladr ∈ lax; (s)% ⊦ (ladr ' + lax).tail = lax; (s)% ⊦ ladr ' + lax ≠ []; (s)% ⊦ @(m, m0) = @(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ (ladr ' + lax).head = ladr; (s)% ⊦ ladr ∈ lax → (lax + lax0).head = lax.head; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%in-14: ⊦ ladr ' + lax = lax0 → ladr ∈ lax0; (forward) from specification list[laddress-list]% ⊦ ladr + lax = ladr ' + lax; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list