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Proof step 46 from proof prepost-cleanup-lpt (previous step)

# lpt4 = n1 + n0, # avol1 = n1 + n0, # lpt3 = n1 + n0, lpt4[n0] = mklp(0, m2, LP_GROUP_NODES, m3), lpt2[n0] = mklp(0, m2, LP_GROUP_NODES, m5), lpt3[n0] = mklp(0, m2, LP_GROUP_NODES, m4), cleanup-lpt(lpt4, n0)[n0] = mklp(0, m2, LP_GROUP_NODES, m3), keyset(gch0) = gc-heap(lpt4, []), keyset(bin-heap(kar, m1)) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch1) = gc-heap(cleanup-lpt(lpt4, n0), []) -- key-index(0, n0), n0 < # lpt2, 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(bin-heap(kar, m1), lpt3), bin-heap-inv(gch1, lpt2), freelist-cons(lpt4, freelist0), freelist-cons(cleanup-lpt(lpt4, n0), freelist), id-idx(cleanup-lpt(lpt4, n0), lpt3), id-idx(lpt3, lpt2), synced(avol1), synced(avol), key-index(0, n0) ∈ gc-heap(cleanup-lpt(lpt4, n0), []), # lpt2 ≤ n1 + n0 ⊦ # gc-heap(cleanup-lpt(lpt4, n0), []) = 0, LP_GROUP_NODES = LP_FREE, gc-heap(cleanup-lpt(lpt4, n0), []) = ∅, m1 = 0, n1 = 0, true ∧ avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4) ∧ id-idx(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], lpt2[n0, mklp(0, 0, LP_FREE, m5)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
# lpt3 = n1 + n0, # avol1 = n1 + n0, # lpt4 = n1 + n0, lpt3[n0] = mklp(0, m2, LP_GROUP_NODES, m4), lpt2[n0] = mklp(0, m2, LP_GROUP_NODES, m5), lpt4[n0] = mklp(0, m2, LP_GROUP_NODES, m3), keyset(gch1) = gc-heap(cleanup-lpt(lpt4, n0), []) -- key-index(0, n0), keyset(bin-heap(kar, m1)) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch0) = gc-heap(lpt4, []), n0 < # avol, n0 < # lpt2, avol-cleanup-lpt-unchanged(avol1, avol, lpt4), awbuf-inv(avol, nobuffer), awbuf-inv(avol1, nobuffer), bin-heap-inv(gch1, lpt2), bin-heap-inv(bin-heap(kar, m1), lpt3), bin-heap-inv(gch0, lpt4), freelist-cons(cleanup-lpt(lpt4, n0), freelist), freelist-cons(lpt4, freelist0), id-idx(lpt3, lpt2), id-idx(cleanup-lpt(lpt4, n0), lpt3), synced(avol), synced(avol1), key-index(0, n0) ∈ gc-heap(cleanup-lpt(lpt4, n0), []), # lpt2 ≤ n1 + n0 ⊦ # gc-heap(cleanup-lpt(lpt4, n0), []) = 0, gc-heap(cleanup-lpt(lpt4, n0), []) = ∅, m1 = 0, n1 = 0, avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4) ∧ id-idx(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], lpt2[n0, mklp(0, 0, LP_FREE, m5)])

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)% ⊦ LP_FREE ≠ LP_GROUP_NODES; (s)%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)