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Theorem subset-size

⊦ # st0 < # st → ¬ st ⊆ st0

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 17
Used lemmas: In-empty, subset-empty-01, empty-01, size, notin-del-notin, Size-insert, subset-elem-eq-01, subset-put-01, in-pair, subset-put-02, ins, size-in, empty, Size-empty, subset-empty, gen-04,
Used spec theorems:
- Used simplifier rules:
  - nat-basic1/zero-01
  - nat-basic1/f
  - nat-basic2/s
  - nat/pred-03
  - nat/lels
  - nat/lels-01
  - nat-basic1/one-01
  - nat/lez
  - nat/ls-02
  - nat/let
  - nat/le-add
  - nat-basic2/a
  - nat-basic2/c