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Theorem precedesex-pushix
⊦ precedes∃(ixs, x) ∧ inv(ixs, n) ∧ n < # x → (¬ precedes∃(pushx(n, ixs, x), x) ↔ false)
Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp,
Comment:
Used by:
precedesex-solixh
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 18
Proof steps: 46
Used lemmas:
precedes-def
,
precedesex-2
,
precedesex-rec1
,
precedesex-prepend
,
allls-rec
,
pushx-rec
,
inv-rec
,
precedesex-rec0
,
pushx-base
,
precedesex-base
,
inv-base
,
Used spec theorems:
Used simplifier rules:
list-data
/
l
list-data
/indexseq/
elim-list-c
nat-basic1
/
f
nat-basic1
/
lf-01
nat-basic1
/
lf-02
list
/indexseq-stackseq/
c-03
list
/indexseq-stackseq/
app
list
/indexseq/
app
list
/indexseq-stackseq/
c
list
/indexseq-stackseq/
in-17
list
/indexseq-stackseq/
in-append
nat-basic2
/
succ
oelem
/indexseq/
transitivity
nat-basic1
/
lf
list
/indexseq-stackseq/
in-14
list
/indexseq/
e-01
list
/indexseq/
c
list
/indexseq/
in-17
list
/indexseq/
in-append
list
/indexseq/
a
list
/indexseq/
in-14
list
/indexseq-stackseq/
a
list
/indexseq-stackseq/
c-06