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Proof step 9 from proof abs-nodes-beyond-no-address-h (previous step)

@(m0, m1) ∈ lax, # buf + m ≤ m0, ∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, nd ' + x0, lax, boolvar) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, nd) ∧ abs-nodes(buf1, m + # buf0, x0, lax.tail, boolvar)), ∀ buf0, m, x, lax, boolvar, m0, m1. # buf0 < # buf → abs-nodes(buf0, m, x, lax, boolvar) ∧ @(m0, m1) ∈ lax ∧ # buf0 + m ≤ m0 → false ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
@(m0, m1) ∈ lax, (# buf1 + # buf0) + m ≤ m0, abs-padding(buf1) ∧ abs-nodes(buf0, m + # buf1, nd ' + x0, lax, boolvar) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf1 ∧ abs-node(buf1, nd) ∧ abs-nodes(buf0, lax.head.off + # buf1, x0, lax.tail, boolvar), ∀ buf2, m, x, lax, boolvar, m0, m1. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x, lax, boolvar) ∧ @(m0, m1) ∈ lax ∧ # buf2 + m ≤ m0 → false ⊦

Rule argument

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)