recognition /
Foundation /
Foundation.UniversalForcing.ModularRealization /
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formal statement (Lean)
26 theorem zmodCost_symm {n : ℕ} (a b : ZMod n) : zmodCost a b = zmodCost b a := by
proof body
Tactic-mode proof.
27 by_cases h : a = b
28 · subst h; simp [zmodCost]
29 · have h' : b ≠ a := by intro hb; exact h hb.symm
30 simp [zmodCost, h, h']
31
32 /-- Interpret `LogicNat` in `ZMod n` by the usual coercion of its index. -/
used by (3)
From the project-wide theorem graph. These declarations reference this one in their body.
modularRealization
in IndisputableMonolith.Foundation.UniversalForcing.ModularRealization
decl_use
strictModularRealization
in IndisputableMonolith.Foundation.UniversalForcing.Strict.Modular
decl_use
zmodCost_symm
in IndisputableMonolith.Foundation.UniversalForcing.Strict.Modular
decl_use
depends on (9)
Lean names referenced from this declaration's body.
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
LogicNat
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
of
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
zmodCost
in IndisputableMonolith.Foundation.UniversalForcing.ModularRealization
decl_use
zmodCost
in IndisputableMonolith.Foundation.UniversalForcing.Strict.Modular
decl_use
zmodCost_symm
in IndisputableMonolith.Foundation.UniversalForcing.Strict.Modular
decl_use
of
in IndisputableMonolith.Information.PhysicsComplexityStructure
decl_use