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Proof step 7 from proof bin-heap-inv-cleanup-lpt (previous step)

⊦ bin-heap-inv(bin-heap(kar, m), lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))) ↔ m ≤ # kar ∧ no-dups-idx(kar, m) ∧ valid-idx(kar, lpt, m) ∧ 2exp-size(# kar) ∧ heap-order(kar, m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ bin-heap-inv(bh, lpt) ↔ bh.size ≤ # bh.ar ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, lpt, bh.size) ∧ 2exp-size(# bh.ar) ∧ heap-order(bh.ar, bh.size)
Proof step 9:
⊦ bin-heap(kar, m).size ≤ # bin-heap(kar, m).ar ∧ no-dups-idx(bin-heap(kar, m).ar, bin-heap(kar, m).size) ∧ valid-idx (bin-heap(kar, m).ar, lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp)), bin-heap(kar, m).size) ∧ 2exp-size(# bin-heap(kar, m).ar) ∧ heap-order(bin-heap(kar, m).ar, bin-heap(kar, m).size) ↔ m ≤ # kar ∧ no-dups-idx(kar, m) ∧ valid-idx(kar, lpt, m) ∧ 2exp-size(# kar) ∧ heap-order(kar, m)

Rule argument

spec: bin-min-heap-prepost, inst: gc-heap-rename-gc-heap-base name: bin-heap-inv-def seq: ⊦ bin-heap-inv(bh, lpt) ↔ bh.size ≤ # bh.ar ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, lpt, bh.size) ∧ 2exp-size(# bh.ar) ∧ heap-order(bh.ar, bh.size) subst: [lpt, bh] → [lpt .map (λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx) ;lp ) ), bin-heap(kar, m)] flags: <all paths>

Additional information

Used terms: lpt .map (λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx) ;lp ) ), bin-heap(kar, m)