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Theorem contains-subspec-better
⊦ contains(str0, ty, ty0) ∧ type∃(str, ty) ∧ same-subclasses-contains(ty .jtelemtype .class, str, str0) → contains(str, ty, ty0)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
same-subclasses-contains-trans
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 72
Proof steps: 179
Used lemmas:
contains-array-elemtype-06
,
contains-type-def
,
same-subclasses-forward
,
contains-not-hasclasstype-level-01
,
same-subclasses-contains-typeex-02
,
same-subclasses-all-def
,
contains-type-rec
,
contains-one
,
contains-rec-01
,
same-subclasses-contains-typeex-01
,
contains-typeex-05
,
contains-typeex
,
same-subclasses-contains-typeex
,
contains-type-def-nodups
,
Used spec theorems:
typefuns
/
typeex
typefuns
/
le-noreftype
typefuns
/
array-le
junkrefs
/
same-subclasses-one-def
typefuns
/
tdnameex-06
typefuns
/
tdnameex-03
typefuns
/
tdname+ex-def
junkrefs
/
same-subclasses-tdnameex-03
typefuns
/
jtelemtype-01
junkrefs
/
same-subclasses-tdnameex-05
typefuns
/
subbasic1
typefuns
/
typeex-def
typefuns
/
has-classtype
javatype
/
ex-03
list
/javatypes/
firsteq-01
Used simplifier rules:
typefuns
/
subclass
classnamefuns
/
le-reflexive
typefuns
/
jtelemtype
typefuns
/
tdnameex-02
junkrefs
/
same-subclasses-tdnameex-03
typefuns
/
typeex
list
/javatypes/
len
list
/javatypes/
len-02
nat-basic2
/
s
nat-basic1
/
ref-1
nat-basic2
/
a
nat-basic2
/
c
typefuns
/
isreftype-05
typefuns
/
transitivity
typefuns
/
tdnameex
typefuns
/
classex-notpredef
typefuns
/
classex-nointerface
typefuns
/
classex-03
typefuns
/
classex
classnamefuns
/
le-object
typefuns
/
jtclass
typefuns
/
subtype-object
javatype
/
sel-02
typefuns
/
elemtype-04
typefuns
/
tdname+predef-01
typefuns
/
isreftype-04
javatype
/
test-09
typefuns
/
hasct-05
typefuns
/
typeex-array
javatype
/
elim-01
javatype
/
diff-01
typefuns
/
reftype
typefuns
/
elemtype-rec
typefuns
/
hasclass-no
junkrefs
/
same-subclasses-tdnameex-01
typefuns
/
jtelemtype-01
list
/javatypes/
in-06
list
/javatypes/
e-01
list
/javatypes/
in-08
list
/javatypes/
fr
list
/javatypes/
Nil
list
/javatypes/
c-03
list
/javatypes/
ni
list
/javatypes/
inapp-07
fieldspec
/
sel-03
typefuns
/
interfaceex-noclass
typefuns
/
classex-02
typefuns
/
interfaceex-notpredef
typefuns
/
tdnameex-07
typefuns
/
hasct-04
javatype
/
test-10
typefuns
/
jtelemtype-class
typefuns
/
reftype-class
typefuns
/
class-le
typefuns
/
tdnameex-06
typefuns
/
typeex-class
javatype
/
elim-02
javatype
/
diff
list-dup
/javatypes/
e-01
list
/javatypes/
in-empty
list
/javatypes/
c-05
list
/javatypes/
app
list
/javatypes/
in-17
list
/javatypes/
in-append
list
/javatypes/
in-14
list
/javatypes/
in-15
list
/javatypes/
c
list-data
/javatypes/
elim-list-c
fieldspec
/
elim
list
/javatypes/
e-02
list
/javatypes/
app-02-ant
list
/javatypes/
e
list
/javatypes/
a
list-dup
/javatypes/
dups-cons
list
/javatypes/
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