surjective_stableUnderComposition

English

Surjectivity is stable under composition: if f and g are surjective, then g ∘ f is surjective.

Русский

Суръективность сохраняется под композицию: если f и g сюръективны, то g ∘ f сюръективен.

LaTeX

$$$$ \forall R S T [\mathrm{CommRing} R] [\mathrm{CommRing} S] [\mathrm{CommRing} T](f : R \to+* S)(g : S \to+* T), \; \mathrm{Surjective}(f) \wedge \mathrm{Surjective}(g) \Rightarrow \mathrm{Surjective}(g \circ f). $$$$

Lean4

theorem surjective_stableUnderComposition : StableUnderComposition surjective := by introv R hf hg; exact hg.comp hf

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