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Theorem rem-preserves-monls

⊦ mon<(nσ) → (¬ mon<(rem(nσ, np)) ↔ false)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 15
Proof steps: 29
Used lemmas: monls-to, monls-mon-implies-monls, monls-ls, monls-def, monls-append1,
Used spec theorems:
- list/natstream/lastdiv-rew
- stream/natstream/get-append-ls
- mon-lim-filter-count/natstream/rem-member1-fin
- mon-lim-filter-count/natstream/rem-inf
- mon-lim-filter-count/natstream/mon-remfun
Used simplifier rules:
- stream/natstream/empty
- mon-lim-filter-count/natstream/rem-base
- mon-lim-filter-count/natstream/rem-rec
- stream/natstream/append-finfin
- stream/natstream/append-empty
- list/natstream/len
- nat/lels
- stream/natstream/get-append-ls
- nat-inf/add-all-zero
- nat-inf/add-ls-cancel-num-04
- list-del/natstream/one-03
- nat/zero
- nat/cancel-01
- nat-inf-basic/sel
- nat-inf/prime-add-fin
- nat-inf-basic/disj
- nat-inf/eqls-succ
- nat-inf/ls-notlssucc
- stream/natstream/sel-fin
- stream/natstream/get-append-notls
- list-data/natstream/l
- nat-basic1/f
- nat-basic2/s
- nat-inf/inf-inseq-reduce
- stream/natstream/size-append
- stream/natstream/size-fin
- list/natstream/len-02
- stream/natstream/append-assoc
- nat-inf/less-succ-leq
- nat-inf/less-fin
- nat-basic1/ref-1
- nat-inf/add-assoc
- nat-inf/add-comm
- stream/natstream/get-append2-fin
- list-del/natstream/get-butlast
- list/natstream/a
- list-del/natstream/get-last-03
- nat-basic2/c
- nat-basic2/a
- nat-inf/add-fin
- nat/le-ls-simp