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Proof step 106 from proof prepost-cleanup-lpt (previous step)

# lpt4 = n2 + n0, # avol1 = n2 + n0, # lpt3 = n2 + n0, lpt3[n0] = mklp(0, m1, lpf, m2), keyset(gch0) = gc-heap(lpt4, []), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), avol-cleanup-lpt-unchanged(avol1, avol, lpt4), awbuf-inv(avol1, nobuffer), awbuf-inv(avol, nobuffer), bin-heap-inv(gch0, lpt4), bin-heap-inv(gch, lpt3), freelist-cons(lpt4, freelist0), freelist-cons(cleanup-lpt(lpt4, n0), freelist), id-idx(cleanup-lpt(lpt4, n0), lpt3), synced(avol1), synced(avol), # avol ≤ n0 ⊦ lpf = LP_GROUP_NODES, lpf = LP_FREE, n2 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: persistence-base name: avol-cleanup-lpt-unchanged seq: ⊦ avol-cleanup-lpt-unchanged(avol0, avol1, lpt) ↔ # avol0 = # avol1 ∧ # avol0 = # lpt ∧ (∀ n. n < # avol0 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n]) subst: [lpt, avol1, avol0] → [lpt4, avol, avol1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m + m0 ≤ m ↔ m0 = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: lpt4, avol, avol1