Theorems · Theorem · nonassociative algebras
RootPairing.pairingIn.congr_simp
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_4} {N : Type u_5} [inst : CommRing R] [inst_1 : AddCommGroup M]
[inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] (P P_1 : RootPairing ι R M N) (e_P : P = P_1)
(S : Type u_6) [inst_5 : CommRing S] [inst_6 : Algebra S R] [inst_7 : P.IsValuedIn S] (i i_1 : ι),
i = i_1 → ∀ (j j_1 : ι), j = j_1 → P.pairingIn S i j = P_1.pairingIn S i_1 j_1- Cited by
- 3 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- RootPairingstatement and proof · cited by 710
- RootPairing.IsValuedInstatement and proof · cited by 108
- RootPairing.pairingInstatement and proof · cited by 100
Cited by3
Results whose statement or proof uses this declaration.
- RootPairing.pairingIn_pairingIn_mem_set_of_isCrystal_of_isRedproof · cited by 6
- RootPairing.GeckConstruction.lie_h_eproof · cited by 2
- RootPairing.GeckConstruction.ω_mul_hproof · cited by 2