recognition /
Foundation /
Foundation.ArithmeticFromLogic /
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formal statement (Lean)
235 theorem fromNat_toNat : ∀ n : LogicNat, fromNat (toNat n) = n := by
proof body
Term-mode proof.
236 intro n
237 induction n with
238 | identity => rfl
239 | step n ih =>
240 show fromNat (toNat (succ n)) = succ n
241 rw [toNat_succ, fromNat_succ, ih]
242
used by (7)
From the project-wide theorem graph. These declarations reference this one in their body.
add_left_cancel
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
embed_injective
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
eq_iff_toNat_eq
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
equivNat
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
le_antisymm
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
toNat_le
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
fromInt_toInt
in IndisputableMonolith.Foundation.IntegersFromLogic
decl_use
depends on (11)
Lean names referenced from this declaration's body.
step
in IndisputableMonolith.Complexity.CellularAutomata
decl_use
fromNat
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
fromNat_succ
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
LogicNat
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
succ
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
toNat
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
toNat_succ
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
identity
in IndisputableMonolith.Foundation.ObserverForcing
decl_use
fromNat
in IndisputableMonolith.LedgerUnits
decl_use
succ
in IndisputableMonolith.RRF.Core.Vantage
decl_use
identity
in IndisputableMonolith.RRF.Foundation.VantageCategory
decl_use