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Proof step 28 from proof prepost-cleanup-lpt (previous step)

# lpt4 = n1 + n0, # avol1 = n1 + n0, # lpt3 = n1 + n0, lpt3[n0] = mklp(0, m3, LP_GROUP_NODES, m4), gch = bin-heap(kar, m0), keyset(gch0) = gc-heap(lpt4, []), keyset(bin-heap(kar, m0)) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch1) = gc-heap(cleanup-lpt(lpt4, n0), []) -- key-index(0, n0), lpt1 = lpt3, n0 < # lpt2, n0 < # lpt2[n0, lpt2[n0].flags:= LP_FREE], 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, m0), lpt3), bin-heap-inv(gch1, lpt2), freelist-cons(cleanup-lpt(lpt4, n0), freelist), freelist-cons(lpt4, freelist0), id-idx(cleanup-lpt(lpt4, n0), lpt3), id-idx(lpt1, lpt2), synced(avol1), synced(avol), key-index(0, n0) ∈ gc-heap(cleanup-lpt(lpt4, n0), []) ⊦ ⟪awbuf_unmap#(n0, adr, m, log, lpt0, ns, nobuffer, isbuf; avol); n := n0 + 1⟫ ( n ≤ # lpt2[n0, lpt2[n0].flags:= LP_FREE] [n0, mklp (lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].ref-size, 0, lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].flags, lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].gcheapidx) ] ∧ # lpt2[n0, lpt2[n0].flags:= LP_FREE] [n0, mklp (lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].ref-size, 0, lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].flags, lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].gcheapidx) ] = # lpt4 ∧ id-idx (cleanup-lpt(lpt4, n), lpt2[n0, lpt2[n0].flags:= LP_FREE] [n0, mklp (lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].ref-size, 0, lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].flags, lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].gcheapidx) ]) ∧ awbuf-inv(avol, nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol, lpt4) ∧ freelist-cons(cleanup-lpt(lpt4, n), freelist + n0 ') ∧ keyset(gch1) = gc-heap(cleanup-lpt(lpt4, n), []) ∧ bin-heap-inv (gch1, lpt2[n0, lpt2[n0].flags:= LP_FREE] [n0, mklp (lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].ref-size, 0, lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].flags, lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].gcheapidx) ]) ∧ # lpt2[n0, lpt2[n0].flags:= LP_FREE] [n0, mklp (lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].ref-size, 0, lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].flags, lpt2[n0, lpt2[n0].flags:= LP_FREE][n0].gcheapidx) ] < n1 + n), # gc-heap(cleanup-lpt(lpt4, n0), []) = 0, gc-heap(cleanup-lpt(lpt4, n0), []) = ∅, m0 = 0, n1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
# lpt4 = n1 + n0, # avol1 = n1 + n0, # lpt3 = n1 + n0, lpt3[n0] = mklp(0, m3, LP_GROUP_NODES, m4), keyset(gch0) = gc-heap(lpt4, []), keyset(bin-heap(kar, m0)) = gc-heap(cleanup-lpt(lpt4, n0), []), keyset(gch1) = gc-heap(cleanup-lpt(lpt4, n0), []) -- key-index(0, n0), # gc-heap(cleanup-lpt(lpt4, n0), []) ≠ 0, gc-heap(cleanup-lpt(lpt4, n0), []) ≠ ∅, m0 ≠ 0, n1 ≠ 0, n0 < # lpt2, 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, m0), lpt3), bin-heap-inv(gch1, lpt2), freelist-cons(cleanup-lpt(lpt4, n0), freelist), freelist-cons(lpt4, freelist0), 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), []) ⊦ ⟪awbuf_unmap#(n0, adr, m, log, lpt0, ns, nobuffer, isbuf; avol); n := n0 + 1⟫ ( n ≤ # lpt2 ∧ # lpt2 = # lpt4 ∧ id-idx(cleanup-lpt(lpt4, n), lpt2[n0, mklp(lpt2[n0].ref-size, 0, LP_FREE, lpt2[n0].gcheapidx)]) ∧ awbuf-inv(avol, nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol, lpt4) ∧ freelist-cons(cleanup-lpt(lpt4, n), freelist + n0 ') ∧ keyset(gch1) = gc-heap(cleanup-lpt(lpt4, n), []) ∧ bin-heap-inv(gch1, lpt2[n0, mklp(lpt2[n0].ref-size, 0, LP_FREE, lpt2[n0].gcheapidx)]) ∧ # lpt2 < n1 + n)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)%m < # lpt ⊦ lpt[m, lp][m, lp0] = lpt[m, lp0]; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ (lp.flags:= lpf).gcheapidx = lp.gcheapidx; (s)% ⊦ (lp.flags:= lpf).flags = lpf; (s)% ⊦ (lp.flags:= lpf).ref-size = lp.ref-size; (s)% ⊦ m < # lpt → lpt[m, lp][m] = lp; (s)% ⊦ # lpt[n, lp] = # lpt; (s)