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Theorem stutf-alltaken

⊦ stutf(nσ) ∧ ⌜m⌝ < # nσ ∧ n ≤ nσ[m] → (∃ m0. m0 ≤ m ∧ nσ[m0] = n)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: inv-get-inverse, inv-get-inverse-between, inv-get-inverse-succ, inv-get-lslen, inv-ls-succ, leninv-inf, leninv-succ, lsleninv-1, stutf-maxinf-is-fin,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 16
Used lemmas: stutf-def, stutf-zero,
Used spec theorems:
- Used simplifier rules:
  - stream/natstream/zero-len
  - nat/lez-01
  - nat-inf/add-fin
  - nat-basic2/succ
  - nat-inf/add-comm
  - nat-inf/add-assoc
  - nat-inf/ls-natinf-to-nat-2-1
  - nat-inf/lsle-trans
  - nat/ler
  - nat/les
  - nat-basic1/ref-1
  - nat-basic2/s
  - nat-basic2/oz
  - nat-basic2/eq
  - nat/le-one
  - nat/eqle-one
  - nat/le-ls-simp
  - nat-basic1/lf-01
  - nat-basic1/lf-02
  - nat/lep-02
  - nat/lels-01
  - nat-basic1/f
  - nat/fle
  - nat-basic2/l-02
  - nat-basic2/a
  - nat-basic2/c