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Proof step 59 from proof prepost-cleanup-lpt (previous step)

# avol1 = n1 + n0, # avol = n1 + n0, # lpt4 = n1 + n0, # lpt3 = n1 + n0, lpt4[n] = mklp(m, m0, lpf, m6), 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), avol1[n] = avol[n], 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, n < n1 + n0, 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), id-idx(cleanup-lpt(lpt4, n0), lpt2), synced(avol1), synced(avol), key-index(0, n0) ∈ gc-heap(cleanup-lpt(lpt4, n0), []), # lpt2 ≤ n1 + n0, m ≠ 0 ∨ lpf = LP_FREE ⊦ # gc-heap(cleanup-lpt(lpt4, n0), []) = 0, avol[n] = avol[n0, unmapped][n], gc-heap(cleanup-lpt(lpt4, n0), []) = ∅, m1 = 0, n1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array, inst: avolume name: Put-other seq: ⊦ m ≠ n → avol[n, aleb][m] = avol[m] subst: [m, aleb, n, avol] → [n, unmapped, n0, avol] flags: <all paths>

Additional information

Used simplifier rules: id-idx-cleanup-lpt-backwards-fwd: n < # lpt0 ⊦ id-idx(cleanup-lpt(lpt0, n), lpt1) ∧ lpt0[n] = mklp(m0, m1, lpf0, m2) ∧ lpt1[n] = mklp(n0, n1, lpf1, n2) → m0 = n0 ∧ m1 = n1 ∧ lpf0 = lpf1;% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ 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%m < # avol ⊦ avol[m, aleb][m] = aleb; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)% ⊦ LP_FREE ≠ LP_GROUP_NODES; (s) Used terms: n, unmapped, n0, avol