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Proof step 7 from proof prepost-gcheap-add-log (previous step)

keyset(gch0) = gc-heap(lpt1, nx), keyset(gch) = gc-heap(lpt, log), ki = key-index(lpt[m].ref-size, m), log = log0, log1 = nx, lpt0 = lpt1, m = log.head, m < # lpt, 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 ⊦ ⟪gc_heap_insert#(ki; gch, lpt); log := log.tail⟫ ( ( bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log) ∧ id-idx(lpt1, lpt) ∧ ¬ dups(log) ∧ (∀ n. n ∈ log → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES)) ∧ # log < # log0), log = [], dups(nx), dups(log)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
keyset(gch) = gc-heap(lpt1, log0), keyset(gch0) = gc-heap(lpt1, nx), log0 ≠ [], log0.head < # lpt, bin-heap-inv(gch0, lpt1), bin-heap-inv(gch, lpt), id-idx(lpt1, lpt), ¬ dups(nx), ¬ dups(log0), ∀ n. n ∈ nx → n < # lpt1 ∧ lpt1[n].flags = LP_GROUP_NODES, ∀ n. n ∈ log0 → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ⊦ ⟪gc_heap_insert#(key-index(lpt[log0.head].ref-size, log0.head); gch, lpt); log := log0.tail⟫ ( bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt1, log) ∧ id-idx(lpt1, lpt) ∧ ¬ dups(log) ∧ (∀ n. n ∈ log → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES) ∧ # log < # log0)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ id-idx(lpt0, lpt1) → gc-heap(lpt1, nx) = gc-heap(lpt0, nx); (s)