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Theorem cast-help-comm
0 < i, 0 < i0, i < i0 ⊦ cast(i, cast(i0, j)) = cast(i0, cast(i, j))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
cast-law-comm
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 33
Proof steps: 57
Used lemmas:
cast-def
,
Used spec theorems:
int2bits
/
bits2bits-def
list-del
/bitlista/
lastn-lastn-01
bitopsaux
/
fill-sgn-01
list-last
/bitlista/
mk-first
list
/bitlista/
a
list-last
/bitlista/
mk-plus
list-del
/bitlista/
restN-append
list-del
/bitlista/
rest-mklist
list-del
/bitlista/
lastn-restn-01
nat
/
prop-01
int2bits
/
bits2int-mklist
bitopsaux
/
fill-fill
bitopsaux
/
fillsgn-longer
Used simplifier rules:
list-del
/bitlista/
lastN-append-01
list-del
/bitlista/
lastn-length-01
bitopsaux
/
fillsgn-empty
list-del
/bitlista/
lastn-mklist-03
int-abs
/
lels-02
nat-basic2
/
z
nat-basic1
/
lf-01
int-abs
/
forward-le-01
nat-basic2
/
l
int-abs
/
lels-03
int-abs
/
zero-gels-01
int-abs
/
forward-le-02
nat
/
elim-sub
nat
/
ls-03
nat
/
lels-02
nat
/
zero-02
nat-basic2
/
l-01
nat
/
fle
int2bits
/
int2int-inj
int-abs
/
zero-gels-04
int-abs
/
lels-04
int2bits
/
int2bits-first-01
nat
/
le-ls-simp
nat
/
sub-ls
nat
/
eq-02
nat-basic2
/
eq-01
intnat
/
labs
nat-basic2
/
succ
list-data
/bitlista/
l
nat-basic1
/
trans-1
nat-basic1
/
trans
list-last
/bitlista/
mk-plus
list
/bitlista/
app-02-ant
list-last
/bitlista/
mk-empty
nat
/
zero-01
int-abs
/
ler
list-del
/bitlista/
restN-zero
nat
/
zero
list
/bitlista/
len
list-last
/bitlista/
mk-len
nat
/
prop-07
nat-basic2
/
a
nat-basic2
/
c
list
/bitlista/
a
int-basic1
/
irref
nat
/
lels-03
int-abs
/
lels
int2bits
/
int2bits-first-02
nat-basic1
/
ls-02
int2bits
/
int2bits-not-empty
nat-basic1
/
f
nat
/
lels-01
list-del
/bitlista/
lastn-length
intnat
/
labs-01
int-abs
/
abs-16
int-abs
/
abs
int-abs
/
lels-01
int-basic1
/
ls-01
bitopsaux
/
lastn-fill-sgn
list-del
/bitlista/
lastN-empty
intnat
/
abs-zero
int2bits
/
bits2bits-def
bitopsaux
/
fill-zero
list-del
/bitlista/
lastN-zero
int-abs
/
forward-le-05
int-basic1
/
forward-pos