The syntax category of binder predicates contains predicates like > 0
, ∈ 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
is shorthand for ∃ x, x < 2 ∧ p x
,
and similarly for other binary operators.
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The notation ∀ x < 2, p x
is shorthand for ∀ x, x < 2 → p x
,
and similarly for other binary operators.
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Declare ∃ x > y, ...
as syntax for ∃ x, x > y ∧ ...
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Declare ∃ x ≥ y, ...
as syntax for ∃ x, x ≥ y ∧ ...
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Declare ∃ x < y, ...
as syntax for ∃ x, x < y ∧ ...
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Declare ∃ x ≤ y, ...
as syntax for ∃ x, x ≤ y ∧ ...
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Declare ∃ x ≠ y, ...
as syntax for ∃ x, x ≠ y ∧ ...
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Declare ∀ x ∈ y, ...
as syntax for ∀ x, x ∈ y → ...
and ∃ x ∈ y, ...
as syntax for
∃ x, x ∈ y ∧ ...
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Declare ∀ x ∉ y, ...
as syntax for ∀ x, x ∉ y → ...
and ∃ x ∉ y, ...
as syntax for
∃ x, x ∉ y ∧ ...
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Declare ∀ x ⊆ y, ...
as syntax for ∀ x, x ⊆ y → ...
and ∃ x ⊆ y, ...
as syntax for
∃ x, x ⊆ y ∧ ...
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Declare ∀ x ⊂ y, ...
as syntax for ∀ x, x ⊂ y → ...
and ∃ x ⊂ y, ...
as syntax for
∃ x, x ⊂ y ∧ ...
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Declare ∀ x ⊇ y, ...
as syntax for ∀ x, x ⊇ y → ...
and ∃ x ⊇ y, ...
as syntax for
∃ x, x ⊇ y ∧ ...
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Declare ∀ x ⊃ y, ...
as syntax for ∀ x, x ⊃ y → ...
and ∃ x ⊃ y, ...
as syntax for
∃ x, x ⊃ y ∧ ...