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Proof step 14 from proof prepost-gcheap-add-log (previous step)

lpt[n0] = mklp(m, m0, lpf, m1), keyset(gch) = gc-heap(lpt1, n0 ' + nx0), keyset(gch0) = gc-heap(lpt1, nx), n0 < # lpt, bin-heap-inv(gch, lpt), bin-heap-inv(gch0, lpt1), id-idx(lpt1, lpt), ∀ n. n = n0 ∨ n ∈ nx0 → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES, ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES ⊦ dups(nx0), dups(nx), n0 ∈ nx0, bin-heap-inv(gch, lpt) ∧ lpt = lpt ∧ gch = gch ∧ key-index(m, n0).idx < # lpt ∧ (∀ ki0. ki0 ∈ keyset(gch) → ki0.idx ≠ key-index(m, n0).idx)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
lpt[ki.idx] = mklp(m, m0, lpf, m1), keyset(gch) = gc-heap(lpt1, ki.idx ' + nx0), keyset(gch0) = gc-heap(lpt1, nx), ki.idx < # lpt, bin-heap-inv(gch, lpt), bin-heap-inv(gch0, lpt1), id-idx(lpt1, lpt), ki ∈ keyset(gch), ∀ n. n = ki.idx ∨ n ∈ nx0 → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES, ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES ⊦ gch.size = 0, dups(nx0), dups(nx), ki.idx ∈ nx0

Rule argument

Additional information

Used simplifier rules: ⊦ bin-heap-inv(bh, lpt) → (keyset(bh) = ∅ ↔ bh.size = 0); (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%ne-01: ⊦ ki ∈ gchs → gchs ≠ ∅; (forward) from specification set-basic[gc-heap-rename-gc-heap-base-keyindex-set]% ⊦ key-index(natkey, m).idx = m; (s)