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Proof step 39 from proof abs-split-by-address-h (previous step)

# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf1, nd), abs-nodes(buf0, m + # buf1, x2, lax + ladr ' + lax1, boolvar0), ∃ buf3, buf1, buf4, x0, a, x1. x2 = x0 + a ' + x1 ∧ # x0 = # lax ∧ buf0 = buf3 + buf1 + buf4 ∧ ladr = @((m + nd.alignedsize + 2 * NODE_HEADER_SIZE) + # buf3, 2 * NODE_HEADER_SIZE + a.alignedsize) ∧ # buf1 = 2 * NODE_HEADER_SIZE + a.alignedsize ∧ abs-node(buf1, 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 40:
# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, # buf2 = 2 * NODE_HEADER_SIZE + a.alignedsize, # x0 = # lax, abs-node(buf1, nd), abs-node(buf2, a), abs-nodes(buf3 + buf2 + buf, m + # buf1, x0 + a ' + x, lax + @((m + # buf1) + # buf3, # buf2) ' + lax1, boolvar0), ∀ 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, x3, a0, x1. nd ' + x0 + a ' + x = x3 + a0 ' + x1 ∧ # x3 = # 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;%c: ⊦ m + n = n + m; from specification nat-basic