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theorem proved term proof

hi_lt_implies_contains_lt

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formal statement (Lean)

 167theorem hi_lt_implies_contains_lt {I : Interval} {b : ℚ} (h : I.hi < b) {x : ℝ}
 168    (hx : I.contains x) : x < (b : ℝ) :=

proof body

Term-mode proof.

 169  lt_of_le_of_lt hx.2 (by exact_mod_cast h)
 170
 171/-- If b ≤ I.lo, then all x in I satisfy b ≤ x -/

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