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formal statement (Lean)
256theorem phi_inv_eq : goldenRatio⁻¹ = goldenRatio - 1 := by
proof body
Term-mode proof.
257 -- φ⁻¹ = -ψ = -(1 - √5)/2 = (√5 - 1)/2 = (1 + √5)/2 - 1 = φ - 1
258 rw [inv_goldenRatio]
259 unfold goldenRatio goldenConj
260 ring
261
used by (6)
From the project-wide theorem graph. These declarations reference this one in their body.
-
phi_inv_eq
in IndisputableMonolith.Foundation.PhiEmergence
decl_use
-
phi_series_sum
in IndisputableMonolith.Foundation.PhiEmergence
decl_use
-
phi_inv_gt
in IndisputableMonolith.Numerics.Interval.PhiBounds
decl_use
-
phi_inv_lt
in IndisputableMonolith.Numerics.Interval.PhiBounds
decl_use
-
phi_inv_eq
in IndisputableMonolith.Unification.YangMillsMassGap
decl_use
-
phi_plus_inv
in IndisputableMonolith.Unification.YangMillsMassGap
decl_use
depends on (2)
Lean names referenced from this declaration's body.
-
phi_inv_eq
in IndisputableMonolith.Foundation.PhiEmergence
decl_use
-
phi_inv_eq
in IndisputableMonolith.Unification.YangMillsMassGap
decl_use