# Documentation

Std.Util.ExtendedBinder

Defines an extended binder syntax supporting ∀ ε > 0, ...∀ ε > 0, ... etc.

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The syntax category of binder predicates contains predicates like > 0, ∈ s∈ s, etc. (: t should not be a binder predicate because it would clash with the built-in syntax for ∀/∃.)

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satisfies_binder_pred% t pred expands to a proposition expressing that t satisfies pred.

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The notation ∃ x < 2, p x∃ x < 2, p x is shorthand for ∃ x, x < 2 ∧ p x∃ x, x < 2 ∧ p x∧ p x, and similarly for other binary operators.

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The notation ∀ x < 2, p x∀ x < 2, p x is shorthand for ∀ x, x < 2 → p x∀ x, x < 2 → p x→ p x, and similarly for other binary operators.

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An extended binder has the form x, x : ty, or x pred where pred is a binderPred like < 2.

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A extended binder in parentheses

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A list of parenthesized binders

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A single (unparenthesized) binder, or a list of parenthesized binders

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The syntax ∃ᵉ (x < 2) (y < 3), p x y∃ᵉ (x < 2) (y < 3), p x y is shorthand for ∃ x < 2, ∃ y < 3, p x y∃ x < 2, ∃ y < 3, p x y∃ y < 3, p x y.

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The syntax ∀ᵉ (x < 2) (y < 3), p x y∀ᵉ (x < 2) (y < 3), p x y is shorthand for ∀ x < 2, ∀ y < 3, p x y∀ x < 2, ∀ y < 3, p x y∀ y < 3, p x y.

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Declares a binder predicate. For example:

binder_predicate x " > " y:term => ($x >$y)

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Missing docs handler for binder_predicate

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Declare ∃ x > y, ...∃ x > y, ... as syntax for ∃ x, x > y ∧ ...∃ x, x > y ∧ ...∧ ...

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Declare ∃ x ≥ y, ...∃ x ≥ y, ...≥ y, ... as syntax for ∃ x, x ≥ y ∧ ...∃ x, x ≥ y ∧ ...≥ y ∧ ...∧ ...

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Declare ∃ x < y, ...∃ x < y, ... as syntax for ∃ x, x < y ∧ ...∃ x, x < y ∧ ...∧ ...

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Declare ∃ x ≤ y, ...∃ x ≤ y, ...≤ y, ... as syntax for ∃ x, x ≤ y ∧ ...∃ x, x ≤ y ∧ ...≤ y ∧ ...∧ ...`

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