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Proof step 84 from proof prepost-cleanup-lpt (previous step)

# 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) ∧ freelist-cons(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], freelist + n0 ') ∧ keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], [])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 85:
lpf0 ≠ LP_GROUP_NODES, lpf1 ≠ LP_GROUP_NODES, n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) → gc-heap(lpt[n, mklp(n0, n1, lpf1, n2)], nx) = gc-heap(lpt, nx)
Proof step 86:
# 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) ⊦ LP_FREE = LP_GROUP_NODES, lpf = LP_FREE, lpf = LP_GROUP_NODES, n2 = 0, awbuf-inv(avol[n0, unmapped], nobuffer) ∧ avol-cleanup-lpt-unchanged(avol1, avol[n0, unmapped], lpt4) ∧ freelist-cons(cleanup-lpt(lpt4, n0)[n0, mklp(0, 0, LP_FREE, m3)], freelist + n0 ') ∧ keyset(gch) = gc-heap(cleanup-lpt(lpt4, n0), [])

Rule argument

spec: persistence-base name: gc-heap-write-other seq: lpf0 ≠ LP_GROUP_NODES, lpf1 ≠ LP_GROUP_NODES, n < # lpt ⊦ lpt[n] = mklp(m0, m1, lpf0, m2) → gc-heap(lpt[n, mklp(n0, n1, lpf1, n2)], nx) = gc-heap(lpt, nx) subst: [lpf0, m0, m1, m2, nx, n2, lpf1, n1, n0, n, lpt] → [lpf, 0, m1, m3, [], m3, LP_FREE, 0, 0, n0, cleanup-lpt(lpt4, n0)] flags: <all paths>

Additional information

Used simplifier rules: nat-stuff0: ⊦ n = n0 + n1 → (n0 < n ↔ n1 ≠ 0);% ⊦ LP_FREE ≠ LP_GROUP_NODES; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≤ # lpt ⊦ # cleanup-lpt(lpt, n) = # lpt; (s)% ⊦ m ≤ m; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)%n ≤ m, m < # lpt ⊦ cleanup-lpt(lpt, n)[m] = lpt[m]; (s) Used terms: lpf, 0, m1, m3, [], m3, LP_FREE, 0, 0, n0, cleanup-lpt(lpt4, n0)