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Proof step 56 from proof prepost-create-gcheap (previous step)

gc-heap(lpt, log, n) = keyset(gch), gch0 = bin-heap(mkkeyarray(1), 0), log = nx, lpt0 = lpt2, n1 = 0, bin-heap-inv(gch, lpt), id-idx(lpt2, lpt), n ≤ # lpt ⊦ n < # lpt, bin-heap-inv(gch, lpt) ∧ gc-heap(lpt0, nx) = keyset(gch) ∧ id-idx(lpt0, lpt)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 57:
gc-heap(lpt2, nx, # lpt) = keyset(gch), bin-heap-inv(gch, lpt), id-idx(lpt2, lpt) ⊦ gc-heap(lpt2, nx) = keyset(gch)

Rule argument

Additional information

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