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Theorem del-refs-size

⊦ # st ≤ # (st -- r) ↔ ¬ r ∈ st

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 8
Used lemmas: del-subset-del, in-empty, instore-01, instore, del-notin-01,
Used spec theorems:
- store/javastore/size-subset
Used simplifier rules:
- nat-basic2/c
- nat-basic2/a
- nat/lep-01
- nat/let
- store/javastore/empty
- nat/elim-pred-c
- nat/pred-03
- store/javastore/size
- nat/ler
- nat/lels-01
- nat-basic1/ref-1