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Theorem soundness-rec
x ≠ [], x = x0, i ≤ j, max(x) ≤ j ⊦ 〈build_rec#(i; x, to)〉 (to ≠ fail → x0 = depths(to .t, i) + x)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
completeness
,
completeness-rec
,
soundness
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 56
Used lemmas:
build-rec
,
Used spec theorems:
build-base
/
max-concat
Used simplifier rules:
build-base
/
depths-node
list
/intlist/
app
build-base
/
depths-nonnil
int-min
/
max-01
int-basic1
/
irref
int-min
/
max-a
int-min
/
max-c
int-abs
/
succ-02
int-abs
/
lels-01
int-abs
/
forward-le-05
int-abs
/
lels-02
treeorfail
/
disj
treeorfail
/
elim
list
/intlist/
in-11
build-base
/
first-in
intnat
/
abs-pred
int-abs
/
sub-add-05
int-abs
/
le-add
int-abs
/
leone
int-abs
/
lels
int-abs
/
anti
int-basic2
/
ax-04
int-abs
/
forward-lels
build-base
/
max-gt-rec
list
/intlist/
in-17
list
/intlist/
in-append
list
/intlist/
in-14
list
/intlist/
e-01
list
/intlist/
c
list-data
/intlist/
elim-list-c
int-basic1
/
ls-01
int-basic1
/
lst-01
treeorfail
/
sel
build-base
/
depths-leaf
list
/intlist/
fr
list
/intlist/
a
build-base
/
is-empty
int-abs
/
forward-le-01
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
lep
int-abs
/
elim-sub