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Theorem disj-reduce

⊦ disj(T1, T2) → ( ¬ disj(T3, T4) ↔ ¬ (∀ n, m. (n < # T1 ∧ m < # T2 ∧ T1[n] ≠ empty ∧ T2[m] ≠ empty → T1[n].elem ≠ T2[m].elem) → n < # T3 ∧ m < # T4 ∧ T3[n] ≠ empty ∧ T4[m] ≠ empty → T3[n].elem ≠ T4[m].elem))

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 23
Used lemmas: disj,
Used spec theorems:
- Used simplifier rules:
  - slot/elim
  - nat-basic1/f
  - slot/disj