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Theorem max-def
⊦ (n * (n + 1)) / 2 ≤ m ∧ m < ((n + 1) * (n + 2)) / 2 ∧ (m0 * (m0 + 1)) / 2 ≤ m → maxenc(m0, m) = n
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
max-def-01
,
max-rev
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 18
Proof steps: 19
Used lemmas:
maxi-found
,
maxi-rec
,
Used spec theorems:
nat-div
/
square-interval
nat-basic2
/
add-base
nat
/
le-def
nat-div
/
square-ls-02
nat-mult
/
dist
nat-div
/
div-add
Used simplifier rules:
nat-basic2
/
z
nat-div
/
ls-02
nat-div
/
two-zero-01-01
nat-mult
/
square-one
nat-basic1
/
trans
nat-basic1
/
ref-1
nat-basic1
/
ls-02
nat-basic2
/
eq-01
nat
/
eq-02
nat
/
ls-03
nat
/
fle
nat
/
let
nat-basic2
/
one
nat
/
lep
nat
/
cancel-01
nat
/
lep-02
nat-basic1
/
f
nat
/
leprf
nat-basic2
/
add-base
nat
/
lez
nat-div
/
two-loup-12
nat-mult
/
ls-01
nat
/
add-num-03
nat
/
lels-01
nat-basic1
/
lf
nat-basic1
/
trans-1
nat
/
fle-01
nat
/
elim-sub
nat-mult
/
rsucc-02
nat-basic2
/
a
nat-basic2
/
c
nat-mult
/
mult-a
nat-mult
/
mult-c
nat-div
/
mod-mult
nat-div
/
two-rec
nat-div
/
two-mdiv2-02
nat-basic2
/
s
nat
/
succ-01
nat
/
lels
nat
/
le-ls-simp
nat-mult
/
succ
nat-div
/
le-div-to-mult