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Theorem keyset-eq-empty

⊦ bin-heap-inv(bh, ar) → (keyset(bh) = ∅ ↔ bh.size = 0)

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 5
Used lemmas: bin-heap-inv-def, keyset,
Used spec theorems:
- Used simplifier rules:
  - bin-min-heap/elim
  - bin-min-heap-inv/keyset-base
  - nat-basic/succ
  - nat-basic/oz
  - nat-basic/a
  - nat-basic/c
  - nat/succ-01
  - bin-min-heap-inv/keyset-rec
  - set-basic/keyindex-set/ne