Theorems · Theorem · linear algebra
Submodule.coe_scott_continuous
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
OmegaCompletePartialOrder.ωScottContinuous SetLike.coeWe can regard coe_iSup_of_chain as the statement that (↑) : (Submodule R M) → Set M is
Scott continuous for the ω-complete partial order induced by the complete lattice structures.
- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- OmegaCompletePartialOrder.Chainproof · cited by 85
- OmegaCompletePartialOrder.ωScottContinuousstatement · cited by 47
- SetLike.coe_monoproof · cited by 18
- OmegaCompletePartialOrder.Chain.toOrderHomproof · cited by 10
- OmegaCompletePartialOrder.ωScottContinuous.of_monotone_map_ωSupproof · cited by 9
- Submodule.coe_iSup_of_chainproof · cited by 1
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