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Proof step 13 from proof abs-split-by-address-h (previous step)

lax0 + ladr ' = @(m0, m1) ' + lax2, abs-padding(buf1) ∧ abs-nodes(buf0, m + # buf1, nd ' + x2, lax0 + ladr ' + lax1, boolvar0) ∨ m0 = m ∧ m1 = # buf1 ∧ abs-node(buf1, nd) ∧ abs-nodes(buf0, m + # buf1, x2, (lax0 + ladr ' + lax1).tail, boolvar0), ladr = @(m0, m1) ∨ ladr ∈ lax2, @(m0, m1) ∈ lax0 ∨ @(m0, m1) = ladr, ∀ buf2, m, x, lax0, ladr, lax1, boolvar0. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x, lax0 + ladr ' + lax1, boolvar0) → (∃ buf3, buf1, buf4, x0, a, x1. x = x0 + a ' + x1 ∧ # x0 = # lax0 ∧ buf2 = buf3 + buf1 + buf4 ∧ ladr = @(m + # buf3, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf1 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf1, a)) ⊦ ∃ buf4, buf3, buf2, x, a, x0. nd ' + x2 = x + a ' + x0 ∧ # x = # lax0 ∧ buf1 + buf0 = buf4 + buf3 + buf2 ∧ ladr = @(m + # buf4, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf3 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf3, a)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
lax0 + ladr ' = @(m0, m1) ' + lax2, lax0 + ladr ' + lax1 = ladr0 + lax3, @(m0, m1) ∈ lax0 ∨ @(m0, m1) = ladr, ladr = @(m0, m1) ∨ ladr ∈ lax2, abs-padding(buf1) ∧ abs-nodes(buf0, m + # buf1, nd ' + x2, lax0 + ladr ' + lax1, boolvar0) ∨ m0 = m ∧ m1 = # buf1 ∧ abs-node(buf1, nd) ∧ abs-nodes(buf0, m + # buf1, x2, lax3, boolvar0), ∀ buf2, m, x, lax0, ladr, lax1, boolvar0. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x, lax0 + ladr ' + lax1, boolvar0) → (∃ buf3, buf1, buf4, x0, a, x1. x = x0 + a ' + x1 ∧ # x0 = # lax0 ∧ buf2 = buf3 + buf1 + buf4 ∧ ladr = @(m + # buf3, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf1 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf1, a)) ⊦ lax0 + ladr ' + lax1 = [], ∃ buf4, buf3, buf2, x, a, x0. nd ' + x2 = x + a ' + x0 ∧ # x = # lax0 ∧ buf1 + buf0 = buf4 + buf3 + buf2 ∧ ladr = @(m + # buf4, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf3 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf3, a)

Rule argument

spec: list-data, inst: laddress-list name: elim-list-c seq: lax ≠ [] ⊦ ladr = lax.head ∧ lax0 = lax.tail ↔ lax = ladr + lax0 subst: [lax, ladr, lax0] → [lax0 + ladr ' + lax1, ladr0, lax]

Additional information

Used simplifier rules: ⊦ lax + lax0 = [] ↔ lax = [] ∧ lax0 = []; (as)% ⊦ ladr ' + lax ≠ []; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%lax ≠ [] ⊦ ladr = lax.head ∧ lax0 = lax.tail ↔ lax = ladr + lax0; (elim) Used terms: lax0 + ladr ' + lax1, ladr0, lax