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Theorem in-index-in-union

⊦ adr ∈ asar[n] ∧ n < m → adr ∈ union(asar, 0, m)

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: inter-union-empty-one-empty, subseteq-union-diff-one, subseteq-union-one, union-eq-rem-subseteq,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 7
Used lemmas: union-rec,
Used spec theorems:
- nat/le-rec
Used simplifier rules:
- set-basic/address-list-set/size-zero-01
- set-basic/address-list-set/ne-01
- nat-basic/zero-01
- nat/lels
- set-union/address-list-set/unc
- set-union/address-list-set/una
- set-union/address-list-set/unin-01
- nat-basic/add-base
- nat-basic/c
- nat-basic/a
- nat-basic/s-04
- nat-basic/succ
- nat/lez-01
- nat-basic/f