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Theorem gcd-rec2

⊦ m ≤ n → gcd(m, n) = gcd(m, n - m)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: gcd-add, gcd-alldiv-h, gcd-div-both-h, gcd-le-both-h, gcd-mult, gcd-twice, gcd-zero-01-h,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 5
Used lemmas: gcd-sym, gcd-rec1, gcd-c,
Used spec theorems:
- Used simplifier rules:
  - nat/elim-sub
  - nat/lep
  - nat/eq-01
  - nat-basic2/a
  - nat-basic2/c
  - nat/lels-01
  - nat-basic2/l-02