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Theorem in-below
⊦ n ∈ below(ns, m) ↔ n ∈ ns ∧ n < m
Type: A user defined theorem
Validity: The proof is valid.
Features: s,
Comment:
Used by:
below-nonempty
,
below-rem-in
,
below-rem-notin
,
Used by units in proved state:
ubi-asm
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 17
Used lemmas:
below-rec
,
below-base
,
Used spec theorems:
set-basic
/nat-set/
Extension
set-basic
/nat-set/
indef
Used simplifier rules:
set-basic
/nat-set/
In-empty
set-union
/nat-set/
del-in
nat-basic
/
s-04
oelem
/nat-set/
irreflexivity
set-basic
/nat-set/
size-zero
set-basic
/nat-set/
In-insert
set-basic
/nat-set/
ne
nat
/
lels
nat
/
le-ls-simp
nat-basic
/
lf-02
nat
/
fle
set-basic
/nat-set/
Size-insert
nat-basic
/
oz
nat-basic
/
a
nat-basic
/
c
set-basic
/nat-set/
size-zero-01
set-basic
/nat-set/
ne-01
set-basic
/nat-set/
in-03
nat-basic
/
f
set-basic
/nat-set/
in