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Set: add axiom saying that sets are non-empty #27

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Merged
merged 3 commits into from
Jan 31, 2025
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Set: add axiom saying that sets are non-empty #27

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Set: add axiom saying that sets are non-empty
fblanqui Jan 9, 2025
91306a6
update CHANGES
fblanqui Jan 9, 2025
34d9745
Merge remote-tracking branch 'dk/master' into el
fblanqui Jan 31, 2025
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2 changes: 1 addition & 1 deletion CHANGES.md
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Expand Up @@ -11,7 +11,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/).
- Impred: Set constructor o for quantifying over propositions
- Epsilon: Hilbert's ε operator
- List: add iota and indexes
- Set: add ι:Set
- Set: add ι:Set and an axiom el:Π a,τ a saying that every set is non-empty
- Pos, Z: add printing to decimal notation

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4 changes: 4 additions & 0 deletions Set.lp
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Expand Up @@ -10,6 +10,10 @@ injective symbol τ : Set → TYPE; // `t or \tau

builtin "T" ≔ τ;

// We assume that sets are non-empty

symbol el a : τ a;

// Cartesian product

constant symbol × : Set → Set → Set; notation × infix right 10; // \times
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