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formal statement (Lean)
57theorem sensitivity_pos {f : ℝ} (h : 0 < f) : 0 < sensitivity f := by
proof body
Term-mode proof.
58 unfold sensitivity h_0
59 rw [if_neg (not_le.mpr h)]
60 apply div_pos
61 · simp; exact carrier_pos
62 · exact h
63
64/-- Sensitivity is strictly anti-monotonic in `f` (above carrier:
65sensitivity decreases; below: increases). -/
used by (4)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (11)
Lean names referenced from this declaration's body.
-
carrier
in IndisputableMonolith.Engineering.CorticalNeuromodulationDevice
decl_use
-
carrier_pos
in IndisputableMonolith.Engineering.CorticalNeuromodulationDevice
decl_use
-
carrier
in IndisputableMonolith.Engineering.PhantomCoupledGWAntennaSensitivity
decl_use
-
carrier_pos
in IndisputableMonolith.Engineering.PhantomCoupledGWAntennaSensitivity
decl_use
-
h_0
in IndisputableMonolith.Engineering.PhantomCoupledGWAntennaSensitivity
decl_use
-
sensitivity
in IndisputableMonolith.Engineering.PhantomCoupledGWAntennaSensitivity
decl_use
-
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
-
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
-
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
-
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
-
carrier_pos
in IndisputableMonolith.NumberTheory.EulerInstantiation
decl_use