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Proof step 54 from proof prepost-gcheap-add-log (previous step)

keyset(gch) = gc-heap(lpt1, log), keyset(gch0) = gc-heap(lpt1, nx), log = n0 + nx0, bin-heap-inv(gch0, lpt1), bin-heap-inv(gch, lpt), id-idx(lpt1, lpt), # lpt ≤ n0, ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES, ∀ n. n ∈ log → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ⊦ log = [], dups(nx), dups(log)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
keyset(gch0) = gc-heap(lpt1, nx), keyset(gch) = gc-heap(lpt1, n0 ' + nx0), bin-heap-inv(gch, lpt), bin-heap-inv(gch0, lpt1), id-idx(lpt1, lpt), # lpt ≤ n0, ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES, ∀ n. n = n0 ∨ n ∈ nx0 → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ⊦ dups(nx), dups(nx0), n0 ∈ nx0

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ n0 ' + nx ↔ n = n0 ∨ n ∈ nx; (s)% ⊦ dups(n ' + nx) ↔ dups(nx) ∨ n ∈ nx; (ws)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ n ' + nx ≠ []; (s)% ⊦ n + nx = n ' + nx; (s)