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Proof step 37 from proof prepost-create-gcheap (previous step)

# lpt = # lpt1, # lpt1 = n1 + n0, lpt1[n0] = mklp(m, m0, LP_GROUP_NODES, m1), gc-heap(lpt2, log, n0) = keyset(gch), keyset(gch0) = gc-heap(lpt2, log, n0) ++ key-index(m, n0), bin-heap-inv(gch0, lpt), bin-heap-inv(gch, lpt1), id-idx(lpt2, lpt1), # lpt ≤ n1 + n0, ∀ ki. ki ∈ gc-heap(lpt2, log, ki.idx) → ki.idx ≠ n0, ∀ n. n < # lpt → lpt1[n].ref-size = lpt[n].ref-size ∧ lpt1[n].size = lpt[n].size ∧ lpt1[n].flags = lpt[n].flags ⊦ n1 = 0, n0 ∈ log, gc-heap(lpt2, log, n0 + 1) = gc-heap(lpt2, log, n0) ++ key-index(m, n0) ∧ n0 < # lpt

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
# lpt = n1 + n0, # lpt1 = n1 + n0, lpt1[n0] = mklp(m, m0, LP_GROUP_NODES, m1), gc-heap(lpt2, log, n0) = keyset(gch), keyset(gch0) = gc-heap(lpt2, log, n0) ++ key-index(m, n0), bin-heap-inv(gch0, lpt), bin-heap-inv(gch, lpt1), id-idx(lpt2, lpt1), ∀ ki. ki ∈ gc-heap(lpt2, log, ki.idx) → ki.idx ≠ n0, ∀ n. n < n1 + n0 → lpt1[n].ref-size = lpt[n].ref-size ∧ lpt1[n].size = lpt[n].size ∧ lpt1[n].flags = lpt[n].flags ⊦ gc-heap(lpt2, log, n0 + 1) = gc-heap(lpt2, log, n0) ++ key-index(m, n0), n1 = 0, n0 ∈ log

Rule argument

Additional information

Used simplifier rules: ⊦ m < m + n ↔ n ≠ 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)