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Theorem montr-def

⊦ mon(βf) ↔ (∀ σ1, α1, σ2, α2. # σ1 = # α1 + ⌜1⌝ ∧ # σ2 = # α2 + ⌜1⌝ ∧ σ1 ⊑ σ2 ∧ α1 ⊑ α2 → βf(σ1, α1) ⊑ βf(σ2, α2))