Theorems · Theorem · logic and foundations
FirstOrder.Ring.realize_termOfFreeCommRing
∀ {α : Type u_1} {R : Type u_2} [inst : CommRing R] [inst_1 : FirstOrder.Ring.CompatibleRing R] (p : FreeCommRing α)
(v : α → R), FirstOrder.Language.Term.realize v (FirstOrder.Ring.termOfFreeCommRing p) = (FreeCommRing.lift v) p- Cited by
- 5 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- CommRingstatement and proof · cited by 17,173
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- map_mulproof · cited by 1,137
- map_addproof · cited by 964
- map_oneproof · cited by 861
- map_negproof · cited by 378
- FirstOrder.Language.Termproof · cited by 166
- FirstOrder.Language.Functionsproof · cited by 153
- FirstOrder.Language.Term.realizestatement and proof · cited by 81
Cited by5
Results whose statement or proof uses this declaration.
- FirstOrder.realize_genericPolyMapSurjOnOfInjOnproof · cited by 2
- FirstOrder.Field.finite_ACF_prime_not_realize_of_ACF_zero_realizeproof · cited by 2
- FirstOrder.Ring.mvPolynomial_zeroLocus_definableproof · cited by 1
- FirstOrder.Field.realize_genericMonicPolyHasRootproof · cited by 1
- FirstOrder.Field.realize_eqZeroproof · cited by 0