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Theorem mod-nle
⊦ 0 ≤ i0 ∧ i0 < i ∧ 0 < j ∧ 0 < i → (j * i + i0 ≤ j ↔ i = 1 ∧ i0 = 0)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
int-div
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 4
Proof steps: 5
Used lemmas:
dist-sub-split
,
zero-left
,
one-01
,
zero-le
,
commutativity
,
associativity
,
one
,
Used spec theorems:
Used simplifier rules:
int-abs
/
forward-le-01
int-abs
/
forward-le-05
int-abs
/
ler
int-abs
/
lels-01
int-abs
/
lenls
int-abs
/
forward-lels
int-abs
/
forward-le-04
int-abs
/
forward-lele
int-abs
/
lep-01
int-abs
/
sub-le
int-abs
/
bet
int-abs
/
anti
int-abs
/
sub-eq-01
int-basic2
/
add-zero-rev
int-abs
/
sub-add-01
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
sub-eq
int-abs
/
Sub-def
int-basic2
/
add-in