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formal statement (Lean)
105theorem logL_expL (x : LogicReal) : logL (expL x) = x := by
proof body
Term-mode proof.
106 rw [eq_iff_toReal_eq, toReal_logL, toReal_expL]
107 exact Real.log_exp _
108
109/-- Transported hyperbolic cosine definition. -/
depends on (6)
Lean names referenced from this declaration's body.
-
expL
in IndisputableMonolith.Foundation.LogicRealTranscendentals
decl_use
-
logL
in IndisputableMonolith.Foundation.LogicRealTranscendentals
decl_use
-
toReal_expL
in IndisputableMonolith.Foundation.LogicRealTranscendentals
decl_use
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toReal_logL
in IndisputableMonolith.Foundation.LogicRealTranscendentals
decl_use
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eq_iff_toReal_eq
in IndisputableMonolith.Foundation.RealsFromLogic
decl_use
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LogicReal
in IndisputableMonolith.Foundation.RealsFromLogic
decl_use