pith. machine review for the scientific record. sign in
theorem proved term proof

phiLadder_ge_phi

show as:
view Lean formalization →

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

generate prose now

formal statement (Lean)

 167theorem phiLadder_ge_phi {n : ℤ} (hn : 1 ≤ n) : phi ≤ PhiLadder n := by

proof body

Term-mode proof.

 168  unfold PhiLadder
 169  have hge : (1 : ℝ) ≤ phi := le_of_lt one_lt_phi
 170  calc phi = phi ^ (1 : ℤ) := (zpow_one phi).symm
 171    _ ≤ phi ^ n := zpow_le_zpow_right₀ hge hn
 172
 173/-- **φⁿ > 1 for n ≥ 1**. -/

used by (2)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (6)

Lean names referenced from this declaration's body.