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Theorem key-range-replace-branches
⊦ n < m ∧ m ≤ # zbrar0 ∧ # zbrar0 = # zbrar1 ∧ (∀ n0. n0 ≤ n ∧ n0 ≤ m → zbrar0[n0].key = zbrar1[n0].key) → key-range(zbrar0, n, m, ri) = key-range(zbrar1, n, m, ri)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 18
Used lemmas:
range
,
Used spec theorems:
Used simplifier rules:
nat-basic
/
lf-02
nat
/
fle-01
nat-basic
/
zero
nat
/
lez-01
nat
/
lez
oelem
/nat-set/
irreflexivity
nat-basic
/
s-04
nat
/
elim-pred-c
nat-basic
/
succ-03
nat-basic
/
lf-01
nat-basic
/
oz
nat
/
let
nat-basic
/
l-05
nat-basic
/
succ
oelem
/nat-set/
transitivity
nat-basic
/
lf
nat-basic
/
f
nat
/
le-def
nat
/
lep
nat
/
lep-02
nat-basic
/
a
nat-basic
/
c
nat
/
succ-01
nat-basic
/
nls-fst
nat
/
lels-03
nat
/
fle