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theorem proved term proof

lo_ge_implies_contains_ge

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formal statement (Lean)

 172theorem lo_ge_implies_contains_ge {I : Interval} {b : ℚ} (h : b ≤ I.lo) {x : ℝ}
 173    (hx : I.contains x) : (b : ℝ) ≤ x :=

proof body

Term-mode proof.

 174  le_trans (by exact_mod_cast h) hx.1
 175
 176/-- If I.hi ≤ b, then all x in I satisfy x ≤ b -/

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