ExistsImplicationLinter.lean`

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3 declarations, 0 contain sorry, 0 declared as axioms

The Exists Implication Linter

Many misformalisations stem from using a pattern of the form ∃ x, P x → Q instead of ∃ x, P x ∧ Q (e.g. when formalising something of the form "there is positive x such that ..."). This is almost always incorrect (and trivial to prove) since it then suffices to pick an x that does not satisfy P. This linter flags occurrences of this pattern to the user and proposes a corrected syntax.

Imports (4)

Imported by 2 files

def ExistsImplicationLinter.forallToAnd Changes and expression of the form ∀ (h1 : Prop1) (h2 : Prop2) ..., Propn to `Prop1 ∧ Prop2 ∧ line 46 source
Source documentation
Changes and expression of the form ∀ (h1 : Prop1) (h2 : Prop2) ..., Propn to Prop1 ∧ Prop2 ∧ ... ∧ Propn.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Lean.Expr, Lean.Meta.MetaM
Proof uses: Lean.Meta.forallTelescope, Lean.Meta.Context, StateRefT', IO.RealWorld, Lean.Meta.State, Lean.Core.CoreM, Array, Bind.bind, Array.mapM, Lean.Meta.inferType, Array.foldrM, Lean.Meta.mkAppM, Lean.Name.mkStr1, List.toArray, List.cons, List.nil, Array.size, OfNat.ofNat, Nat, Bool.false
8 instances, coercions and auxiliary constants left out.
```
def forallToAnd (expr : Expr) : MetaM Expr :=
…
```
def ExistsImplicationLinter.checkExistsArrow Checks if an expression contains the pattern ∃ x, P x → Q line 54 source
Source documentation
Checks if an expression contains the pattern ∃ x, P x → Q.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Lean.Syntax, Lean.Expr, Lean.Meta.MetaM, Unit
Proof uses: Inhabited.default
1 instances, coercions and auxiliary constants left out.
```
partial def checkExistsArrow (stx : Syntax) (e : Expr) : MetaM Unit := do
…
```
def ExistsImplicationLinter.existsImplicationLinter The existsImplicationLinter detects expressions of the form ∃ a, P a → Q and flags them to the user since those are rarely correct line 83 source
Source documentation
The existsImplicationLinter detects expressions of the form ∃ a, P a → Q and flags them to the user since those are rarely correct.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Lean.Elab.Command.Linter
Proof uses: Lean.Elab.Command.Linter.mk, Lean.Elab.Command.Linter.runTermLinter, Unit, ExistsImplicationLinter.linter.style.existsImplication, Lean.Syntax.Term, Lean.Expr, liftM, ReaderT, Lean.Meta.Context, StateRefT', IO.RealWorld, Lean.Meta.State, Lean.Core.CoreM, StateT, Lean.Meta.MetaM, ExistsImplicationLinter.checkExistsArrow, Lean.TSyntax.raw, List.cons, Lean.SyntaxNodeKind, Lean.Name.mkStr1 and 2 more
5 instances, coercions and auxiliary constants left out.
```
def existsImplicationLinter : Linter where
…
```