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Proof step 25 from proof abs-split-by-address-h (previous step)

abs-nodes(buf, (m + # buf1) + # buf2, nd ' + x2, @(m0, m1) ' + lax3, boolvar0), abs-padding(buf1), abs-padding(buf2), ∃ buf5, buf0, buf4, x0, a, x1. nd ' + x2 = x0 + a ' + x1 ∧ # x0 = # [] ∧ buf = buf5 + buf0 + buf4 ∧ @(m0, m1) = @((m + # buf1 + # buf2) + # buf5, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf0 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf0, a), ∀ buf3, m, x, lax0, ladr, lax1, boolvar0. # buf3 < #(buf1 + buf2 + buf) → abs-nodes(buf3, m, x, lax0 + ladr ' + lax1, boolvar0) → (∃ buf5, buf1, buf4, x0, a, x1. x = x0 + a ' + x1 ∧ # x0 = # lax0 ∧ buf3 = buf5 + buf1 + buf4 ∧ ladr = @(m + # buf5, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf1 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf1, a)) ⊦ ∃ buf5, buf4, buf3, a, x0. nd ' + x2 = a ' + x0 ∧ buf1 + buf2 + buf = buf5 + buf4 + buf3 ∧ @(m0, m1) = @(m + # buf5, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf4 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf4, a)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
# buf3 = 2 * NODE_HEADER_SIZE + a.alignedsize, abs-node(buf3, a), abs-nodes(buf4 + buf3 + buf0, (m + # buf1) + # buf2, a ' + x2, @((m + # buf1 + # buf2) + # buf4, # buf3) ' + lax3, boolvar0), abs-padding(buf2), abs-padding(buf1), ∀ buf5, m, x, lax0, ladr, lax1, boolvar0. # buf5 < #(buf1 + buf2 + buf4 + buf3 + buf0) → abs-nodes(buf5, m, x, lax0 + ladr ' + lax1, boolvar0) → (∃ buf6, buf1, buf4, x0, a, x1. x = x0 + a ' + x1 ∧ # x0 = # lax0 ∧ buf5 = buf6 + buf1 + buf4 ∧ ladr = @(m + # buf6, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf1 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf1, a)) ⊦ ∃ buf5, buf6, buf7, a0, x0. a ' + x2 = a0 ' + x0 ∧ buf1 + buf2 + buf4 + buf3 + buf0 = buf5 + buf6 + buf7 ∧ @((m + # buf1 + # buf2) + # buf4, # buf3) = @(m + # buf5, 2 * NODE_HEADER_SIZE + a0.alignedsize) ∧ # buf6 = 2 * NODE_HEADER_SIZE + a0.alignedsize ∧ abs-node(buf6, a0)

Rule argument

Additional information

Used simplifier rules: ls-abs-node-buf-size: ⊦ abs-node(buf, nd) → # buf = nd.alignedsize + 2 * NODE_HEADER_SIZE;% ⊦ a ∈ b ' + x ↔ a = b ∨ a ∈ x; (s)% ⊦ a ' + x = b ' + y ↔ a = b ∧ x = y; (ws)% ⊦ [] + x = x; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (x + y) + z = x + y + z; from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list% ⊦ @(m, m0) = @(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ # x = 0 ↔ x = []; (s)% ⊦ # [] = 0; (s)