Description: The transitive closure of a relation has a lower bound. (Contributed by RP, 8-May-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | trclfvlb2 | ⊢ ( 𝑅 ∈ 𝑉 → ( 𝑅 ∘ 𝑅 ) ⊆ ( t+ ‘ 𝑅 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | trclfvcotr | ⊢ ( 𝑅 ∈ 𝑉 → ( ( t+ ‘ 𝑅 ) ∘ ( t+ ‘ 𝑅 ) ) ⊆ ( t+ ‘ 𝑅 ) ) | |
2 | trclfvlb | ⊢ ( 𝑅 ∈ 𝑉 → 𝑅 ⊆ ( t+ ‘ 𝑅 ) ) | |
3 | 1 2 2 | trrelssd | ⊢ ( 𝑅 ∈ 𝑉 → ( 𝑅 ∘ 𝑅 ) ⊆ ( t+ ‘ 𝑅 ) ) |