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Theorem size-rem

⊦ (as -- adr).size = as.size - (adr ∈ as ⊃ adr.size;0)

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: refsize-cons-remove-index, refsize-cons-remove-index-0, size-rec-rem,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 5
Used lemmas: size-rec,
Used spec theorems:
- set-basic/address-store/indef
Used simplifier rules:
- set-union/address-store/del-in
- nat/sub-base
- set-basic/address-store/size-zero-01
- set-basic/address-store/ne-01
- address-data/elim
- set-basic/address-store/ne
- set-union/address-store/del-addeq-04
- address-data/sel-05
- nat/eq-01
- nat-basic/a
- nat-basic/c