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Proof step 2 from proof bin-heap-inv-cleanup-lpt (previous step)

⊦ bin-heap-inv(gch, lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))) ↔ bin-heap-inv(gch, lpt)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 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 4:
⊦ bin-heap-inv(gch, lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))) ↔ gch.size ≤ # gch.ar ∧ no-dups-idx(gch.ar, gch.size) ∧ valid-idx(gch.ar, lpt, gch.size) ∧ 2exp-size(# gch.ar) ∧ heap-order(gch.ar, gch.size)

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, gch] flags: <all paths>

Additional information

Used terms: lpt, gch