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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.
-
one_lt_phi
in IndisputableMonolith.Constants
decl_use
-
PhiLadder
in IndisputableMonolith.Foundation.PhiEmergence
decl_use
-
for
in IndisputableMonolith.Foundation.UniversalForcingSelfReference
decl_use
-
one_lt_phi
in IndisputableMonolith.PhiSupport
decl_use
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one_lt_phi
in IndisputableMonolith.PhiSupport.Lemmas
decl_use
-
PhiLadder
in IndisputableMonolith.Unification.YangMillsMassGap
decl_use