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Proof step 7 from proof prepost-create-gcheap (previous step)

gch = bin-heap(mkkeyarray(1), 0), log = nx, lpt0 = lpt, n = 0 ⊦ ⟪while n < # lpt do {/* (prepost-create-gcheap : invariant n ≤ # lpt ∧ bin-heap-inv(gch, lpt) ∧ gc-heap(lpt, log, n) = keyset(gch) ∧ id-idx(lpt`, lpt) wfbound # lpt - n) */; if lpt[n].flags = LP_GROUP_NODES ∧ ¬ n ∈ log then let ki = key-index(lpt[n].ref-size, n) in gc_heap_insert#(ki; gch, lpt); n := n + 1}⟫ (bin-heap-inv(gch, lpt) ∧ gc-heap(lpt0, nx) = keyset(gch) ∧ id-idx(lpt0, lpt))

Heuristic annotation applied rule annotation right

And obtained the following new goals

Proof step 8:
gch = bin-heap(mkkeyarray(1), 0), log = nx, lpt0 = lpt, n = 0 ⊦ n ≤ # lpt ∧ bin-heap-inv(gch, lpt) ∧ gc-heap(lpt, log, n) = keyset(gch) ∧ id-idx(lpt, lpt)
Proof step 11:
gc-heap(lpt, log, n) = keyset(gch), gch0 = bin-heap(mkkeyarray(1), 0), log = nx, lpt = lpt1, lpt0 = lpt2, n = n0, n1 = 0, n < # lpt, bin-heap-inv(gch, lpt), id-idx(lpt2, lpt), n ≤ # lpt ⊦ ⟪if lpt[n].flags = LP_GROUP_NODES ∧ ¬ n ∈ log then let ki = key-index(lpt[n].ref-size, n) in gc_heap_insert#(ki; gch, lpt); n := n + 1⟫ ((n ≤ # lpt ∧ bin-heap-inv(gch, lpt) ∧ gc-heap(lpt, log, n) = keyset(gch) ∧ id-idx(lpt2, lpt)) ∧ # lpt - n < # lpt1 - n0)
Proof step 56:
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)

Rule argument

rule: invariant right arg: bound: # lpt - n inv: n ≤ # lpt ∧ bin-heap-inv(gch, lpt) ∧ gc-heap(lpt, log, n) = keyset(gch) ∧ id-idx(lpt`, lpt) fmapos: right 1 pos: right 1

Additional information

Used formulas: n ≤ # lpt ∧ bin-heap-inv(gch, lpt) ∧ gc-heap(lpt, log, n) = keyset(gch) ∧ id-idx(lpt`, lpt), # lpt - n = # lpt - n