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Proof step 7 from proof abs-nodes-beyond-no-address-h (previous step)

abs-nodes(buf, m, nd ' + x0, lax, boolvar), @(m0, m1) ∈ lax, # buf + m ≤ m0, ∀ buf0, m, x, lax, boolvar, m0, m1. # buf0 < # buf → abs-nodes(buf0, m, x, lax, boolvar) ∧ @(m0, m1) ∈ lax ∧ # buf0 + m ≤ m0 → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ abs-nodes(buf, m, a ' + x, lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ' + x, lax, weak) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax.tail, weak)))
Proof step 9:
@(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 ⊦

Rule argument

spec: <toplevel> name: abs-nodes-rec seq: ⊦ abs-nodes(buf, m, a ' + x, lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ' + x, lax, weak) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax.tail, weak))) subst: [weak, lax, x, a, m, buf] → [boolvar, lax, x0, nd, m, buf] flags: <all paths>

Additional information

Used terms: boolvar, lax, x0, nd, m, buf