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Theorem diff-sub-size
s = s0 \ s1, s1 ⊆ s0 ⊦ # s = # s0 - # s1
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 34
Used lemmas:
del-in
,
Difference
,
del-size
,
diff-add-del
,
diff-e
,
Used spec theorems:
set-basic
/
size-exgr
nat
/
elim-sub
Used simplifier rules:
set-union
/
subdef
set-basic
/
Size-empty
nat-basic2
/
z
nat
/
lez
set-basic
/
Size-insert
set-basic
/
size-zero-01
set-basic
/
ne-01
set-basic
/
In-insert
nat
/
elim-sub
nat
/
lels-01
nat-basic1
/
one-01
nat-basic1
/
lf-01
nat-basic1
/
f
nat-basic2
/
l-01
nat
/
eq-02
nat-basic2
/
eq-01
set-basic
/
In-empty
set-basic
/
Extension
set-basic
/
size-zero-02
nat
/
ler
nat-basic2
/
eq
nat-basic2
/
c
nat-basic2
/
a
nat
/
anti
nat
/
lels
nat
/
succ-01
set-basic
/
eq
set-basic
/
rax