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Proof step 35 from proof abs-split-by-address-h (previous step)

abs-nodes(buf0, m + # buf1, nd ' + x2, @(m0, m1) ' + lax + ladr ' + lax1, boolvar0), abs-padding(buf1), ∃ buf3, buf, buf4, x0, a, x1. nd ' + x2 = x0 + a ' + x1 ∧ # x0 = #(@(m0, m1) ' + lax) ∧ buf0 = buf3 + buf + buf4 ∧ ladr = @((m + # buf1) + # buf3, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf, a), ∀ 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)) ⊦ ∃ buf, buf2, buf3, x, a, x0. nd ' + x2 = x + a ' + x0 ∧ # x = # lax + 1 ∧ buf1 + buf0 = buf + buf2 + buf3 ∧ ladr = @(m + # buf, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf2 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf2, a)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
# x0 = # lax + 1, # buf2 = 2 * NODE_HEADER_SIZE + a.alignedsize, nd ' + x2 = x0 + a ' + x, abs-node(buf2, a), abs-nodes(buf3 + buf2 + buf, m + # buf1, nd ' + x2, @(m0, m1) ' + lax + @((m + # buf1) + # buf3, # buf2) ' + lax1, boolvar0), abs-padding(buf1), nd ∈ x0 ∨ nd = a ∨ nd ∈ x, ∀ buf4, m, x, lax0, ladr, lax1, boolvar0. # buf4 < #(buf1 + buf3 + buf2 + buf) → abs-nodes(buf4, m, x, lax0 + ladr ' + lax1, boolvar0) → (∃ buf3, buf1, buf5, x0, a, x1. x = x0 + a ' + x1 ∧ # x0 = # lax0 ∧ buf4 = buf3 + buf1 + buf5 ∧ ladr = @(m + # buf3, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf1 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf1, a)) ⊦ ∃ buf6, buf5, buf4, x, a0, x0. nd ' + x2 = x + a0 ' + x0 ∧ # x = # lax + 1 ∧ buf1 + buf3 + buf2 + buf = buf6 + buf5 + buf4 ∧ @((m + # buf1) + # buf3, # buf2) = @(m + # buf6, 2 * NODE_HEADER_SIZE + a0.alignedsize) ∧ # buf5 = 2 * NODE_HEADER_SIZE + a0.alignedsize ∧ abs-node(buf5, 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 + y ↔ a ∈ x ∨ a ∈ y; (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%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ m +1 = m + 1; (s)% ⊦ #(ladr ' + lax) = (# lax)+1; (s)