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Theorem size-eq-0

⊦ 0 = as.size ↔ (∀ adr. adr ∈ as → adr.size = 0)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: in-remove-refsize0-refsize-cons, remove-refsize0-refsize-cons, remove-refsize0-subset-refed, size-eq-0-alloc,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 7
Proof steps: 22
Used lemmas: size-rec, size-emp,
Used spec theorems:
- set-basic/address-store/Extension
- set-basic/address-store/indef
Used simplifier rules:
- set-basic/address-store/In-empty
- set-basic/address-store/size-zero
- nat-basic/oz
- set-basic/address-store/In-insert
- address-data/elim
- set-basic/address-store/Size-insert
- nat-basic/s-04
- oelem/nat-set/irreflexivity
- nat-basic/c
- nat-basic/a
- nat-basic/z-01
- set-basic/address-store/size-zero-01
- set-basic/address-store/ne-01
- address-data/sel-05