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Proof step 4 from proof prepost-gcheap-add-log (previous step)

keyset(gch) = gc-heap(lpt, nx), log = nx, lpt0 = lpt, bin-heap-inv(gch, lpt), ∀ n. n ∈ nx → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ⊦ ⟪while log ≠ [] do {/* (prepost-gcheap-add-log : invariant bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log) ∧ id-idx(lpt`, lpt) ∧ ¬ dups(log) ∧ (∀ n. n ∈ log → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES) wfbound # log) */; let m = log.head in let ki = key-index(lpt[m].ref-size, m) in gc_heap_insert#(ki; gch, lpt); log := log.tail}⟫ (log = [] ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt0, []) ∧ id-idx(lpt0, lpt)), dups(nx)

Heuristic annotation applied rule annotation right

And obtained the following new goals

Proof step 5:
keyset(gch0) = gc-heap(lpt1, nx), keyset(gch) = gc-heap(lpt, log), log = log0, log1 = nx, lpt0 = lpt1, 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 ⊦ ⟪let m = log.head in let ki = key-index(lpt[m].ref-size, m) in 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)

Rule argument

rule: invariant right arg: bound: # log inv: bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log) ∧ id-idx(lpt`, lpt) ∧ ¬ dups(log) ∧ (∀ n. n ∈ log → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES) fmapos: right 1 pos: right 1

Additional information

Used simplifier rules: ⊦ id-idx(lpt0, lpt1) → gc-heap(lpt1, nx) = gc-heap(lpt0, nx); (s)% ⊦ ¬ dups([]); (s)% ⊦ ¬ n ∈ []; (s)% ⊦ id-idx(lpt, lpt); (s) Used formulas: bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(lpt, log) ∧ id-idx(lpt`, lpt) ∧ ¬ dups(log) ∧ (∀ n. n ∈ log → n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES), # log = # log