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theorem

hi_le_implies_contains_le

proved
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module
IndisputableMonolith.Numerics.Interval.Basic
domain
Numerics
line
177 · github
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IndisputableMonolith.Numerics.Interval.Basic on GitHub at line 177.

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formal source

 174  le_trans (by exact_mod_cast h) hx.1
 175
 176/-- If I.hi ≤ b, then all x in I satisfy x ≤ b -/
 177theorem hi_le_implies_contains_le {I : Interval} {b : ℚ} (h : I.hi ≤ b) {x : ℝ}
 178    (hx : I.contains x) : x ≤ (b : ℝ) :=
 179  le_trans hx.2 (by exact_mod_cast h)
 180
 181end Interval
 182
 183end IndisputableMonolith.Numerics