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formal statement (Lean)
139private lemma phi_contDiff_succ (H : ℝ → ℝ) (h_cont : Continuous H) {n : ℕ}
140 (h : ContDiff ℝ (n : ℕ∞) H) : ContDiff ℝ ((n + 1 : ℕ) : ℕ∞) (Phi H) := by
proof body
Tactic-mode proof.
141 suffices ContDiff ℝ ((n : ℕ∞) + 1) (Phi H) by exact_mod_cast this
142 rw [contDiff_succ_iff_deriv]
143 exact ⟨phi_differentiable H h_cont,
144 fun h_omega => absurd h_omega (by exact_mod_cast WithTop.coe_ne_top),
145 by rwa [deriv_phi_eq H h_cont]⟩
146
used by (3)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (9)
Lean names referenced from this declaration's body.
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H
in IndisputableMonolith.Algebra.CostAlgebra
decl_use
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deriv_phi_eq
in IndisputableMonolith.Cost.AczelProof
decl_use
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Phi
in IndisputableMonolith.Cost.AczelProof
decl_use
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phi_differentiable
in IndisputableMonolith.Cost.AczelProof
decl_use
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deriv_phi_eq
in IndisputableMonolith.Cost.AczelTheorem
decl_use
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Phi
in IndisputableMonolith.Cost.AczelTheorem
decl_use
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phi_contDiff_succ
in IndisputableMonolith.Cost.AczelTheorem
decl_use
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phi_differentiable
in IndisputableMonolith.Cost.AczelTheorem
decl_use
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H
in IndisputableMonolith.Cost.FunctionalEquation
decl_use