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Proof step 89 from proof prepost-cleanup-lpt (previous step)

# lpt4 = n2 + n0, # avol1 = n2 + n0, # lpt3 = n2 + n0, lpt4[n0] = mklp(0, m1, lpf, m3), lpt3[n0] = mklp(0, m1, lpf, m2), cleanup-lpt(lpt4, n0)[n0] = mklp(0, m1, lpf, m3), keyset(gch0) = gc-heap(lpt4, []), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), n0 < # avol, n0 < # 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) ⊦ lpf = LP_GROUP_NODES, lpf = LP_FREE, n2 = 0, awbuf-inv(avol[n0, unmapped], nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4) ∧ true

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 90:
# lpt3 = n2 + n0, # avol1 = n2 + n0, # lpt4 = n2 + n0, lpt3[n0] = mklp(0, m1, lpf, m2), lpt4[n0] = mklp(0, m1, lpf, m3), keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch0) = gc-heap(lpt4, []), n0 < # avol, avol-cleanup-lpt-unchanged(avol1, avol, lpt4), awbuf-inv(avol, nobuffer), awbuf-inv(avol1, nobuffer), bin-heap-inv(gch, lpt3), bin-heap-inv(gch0, lpt4), freelist-cons(cleanup-lpt(lpt4, n0), freelist), freelist-cons(lpt4, freelist0), id-idx(cleanup-lpt(lpt4, n0), lpt3), synced(avol), synced(avol1) ⊦ lpf = LP_FREE, lpf = LP_GROUP_NODES, n2 = 0, awbuf-inv(avol[n0, unmapped], nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4)

Rule argument

Additional information

Used simplifier rules: nat-stuff0: ⊦ n = n0 + n1 → (n0 < n ↔ n1 ≠ 0);%n ≤ # lpt ⊦ # cleanup-lpt(lpt, n) = # lpt; (s)% ⊦ ¬ m + n < m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%n ≤ m, m < # lpt ⊦ cleanup-lpt(lpt, n)[m] = lpt[m]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m ≤ m; (s)