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Proof step 52 from proof prepost-gcheap-add-log (previous step)

keyset(gch0) = gc-heap(lpt1, nx), keyset(gch) = gc-heap(lpt, log), log = log0, log1 = nx, lpt0 = lpt1, m = log.head, bin-heap-inv(gch0, lpt1), bin-heap-inv(gch, lpt), id-idx(lpt1, lpt), ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES, ∀ n. n ∈ log → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ⊦ log = [], m < # lpt, dups(nx), dups(log)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
keyset(gch0) = gc-heap(lpt1, nx), keyset(gch) = gc-heap(lpt1, log), bin-heap-inv(gch, lpt), bin-heap-inv(gch0, lpt1), id-idx(lpt1, lpt), # lpt ≤ log.head, ∀ n. n ∈ log → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES, ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES ⊦ log = [], dups(log), dups(nx)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ id-idx(lpt0, lpt1) → gc-heap(lpt1, nx) = gc-heap(lpt0, nx); (s)