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Theorem array-exists-first-neq
⊦ ∃ n. n ≤ # ar0 ∧ n ≤ # ar1 ∧ subarray(ar0, 0, n) = subarray(ar1, 0, n) ∧ (n ≠ # ar0 ∧ n ≠ # ar1 → ar0[n] ≠ ar1[n])
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
lexicographic-total
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 11
Proof steps: 28
Used lemmas:
ls-at-subarray
,
Used spec theorems:
array-copy
/
subarray-subarray-elim
array
/gearray/
Extension
Used simplifier rules:
nat-basic2
/
eq
nat
/
anti
nat
/
fle-01
nat-basic1
/gearray/
ls-02
nat
/
lep-02
nat
/
ler
nat
/
let
nat-basic2
/
l-02
nat-basic1
/gearray/
lf-02
nat
/
le-ls-simp
nat
/
lels
nat-basic2
/
oz
nat-basic2
/
ax-08
nat
/
lep
nat
/
lels-02
nat-basic1
/gearray/
neq-01
nat
/
eqle-one
nat-basic1
/gearray/
lf
nat-basic1
/gearray/
trans-1
nat-basic1
/gearray/
lf-01
nat
/
ls-le-simp
nat
/
elim-pred-c
nat
/
succ-01
nat
/
ls-02
array-copy
/
size-subarray
nat-basic1
/gearray/
one-01
nat
/
lels-01
nat
/
ls-01
nat-basic2
/
s
nat-basic1
/gearray/
ref-1
nat-basic2
/
a
nat-basic2
/
c
array
/gearray/
Size-mkarray
nat-basic1
/gearray/
f
array-copy
/
subarray-zero
nat
/
lez
array-copy
/
subarray-elim
nat
/
lez-01