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define _⇒_
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fredrik-bakke committed Dec 12, 2023
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2 changes: 1 addition & 1 deletion MIXFIX-OPERATORS.md
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Expand Up @@ -178,7 +178,7 @@ Below, we outline a list of general rules when assigning associativities.
| 15 | Parametric multiplicative operators like `_×_`,`_×∗_`, `_∧_`, `_∧∗_`, function composition operators like `_∘_`,`_∘∗_`, `_∘e_`, and `_∘iff_`, concatenation operators like `_∙_` and `_∙h_` |
| 10 | Parametric additive operators like `_+_`, `_∨_`, `_∨∗_`, list concatenation, monadic bind operators for the type checking monad |
| 6 | Parametric relational operators like `_=_`, `_~_`, `_≃_`, and `_↔_`, elementhood relations, subtype relations |
| 5 | Directed function type-like formation operators, e.g. `_→∗_` and `_↪_` |
| 5 | Directed function type-like formation operators, e.g. `_⇒_`, `_→∗_`, `_↠_`, `_↪_`, `_↪ᵈ_`, and `_⊆_` |
| 3 | The pairing operators `_,_` and `_,ω_` |
| 0-1 | Reasoning syntaxes |
| -∞ | Function type formation `_→_` |
3 changes: 3 additions & 0 deletions src/foundation-core/propositions.lagda.md
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Expand Up @@ -315,6 +315,9 @@ implication-Prop P Q = hom-Prop P Q
type-implication-Prop :
{l1 l2 : Level} Prop l1 Prop l2 UU (l1 ⊔ l2)
type-implication-Prop P Q = type-hom-Prop P Q

infixr 5 _⇒_
_⇒_ = implication-Prop
```

### The type of equivalences between two propositions is a proposition
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