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5. Preview Relationships🔗

Definition5.1
✓L∃∀N
Used by 2
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Lemma 5.2
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Target statement with associated Lean code.

Lean code for Definition5.1●1 definition
  • defdefined in Init/Prelude.lean
    complete
    def Nat.addNat.add : Nat → Nat → NatAddition of natural numbers, typically used via the `+` operator.
    
    This function is overridden in both the kernel and the compiler to efficiently evaluate using the
    arbitrary-precision arithmetic library. The definition provided here is the logical model.
     : NatNat : TypeThe natural numbers, starting at zero.
    
    This type is special-cased by both the kernel and the compiler, and overridden with an efficient
    implementation. Both use a fast arbitrary-precision arithmetic library (usually
    [GMP](https://gmplib.org/)); at runtime, `Nat` values that are sufficiently small are unboxed.
     → NatNat : TypeThe natural numbers, starting at zero.
    
    This type is special-cased by both the kernel and the compiler, and overridden with an efficient
    implementation. Both use a fast arbitrary-precision arithmetic library (usually
    [GMP](https://gmplib.org/)); at runtime, `Nat` values that are sufficiently small are unboxed.
     → NatNat : TypeThe natural numbers, starting at zero.
    
    This type is special-cased by both the kernel and the compiler, and overridden with an efficient
    implementation. Both use a fast arbitrary-precision arithmetic library (usually
    [GMP](https://gmplib.org/)); at runtime, `Nat` values that are sufficiently small are unboxed.
    
    def Nat.addNat.add : Nat → Nat → NatAddition of natural numbers, typically used via the `+` operator.
    
    This function is overridden in both the kernel and the compiler to efficiently evaluate using the
    arbitrary-precision arithmetic library. The definition provided here is the logical model.
     : NatNat : TypeThe natural numbers, starting at zero.
    
    This type is special-cased by both the kernel and the compiler, and overridden with an efficient
    implementation. Both use a fast arbitrary-precision arithmetic library (usually
    [GMP](https://gmplib.org/)); at runtime, `Nat` values that are sufficiently small are unboxed.
     → NatNat : TypeThe natural numbers, starting at zero.
    
    This type is special-cased by both the kernel and the compiler, and overridden with an efficient
    implementation. Both use a fast arbitrary-precision arithmetic library (usually
    [GMP](https://gmplib.org/)); at runtime, `Nat` values that are sufficiently small are unboxed.
     → NatNat : TypeThe natural numbers, starting at zero.
    
    This type is special-cased by both the kernel and the compiler, and overridden with an efficient
    implementation. Both use a fast arbitrary-precision arithmetic library (usually
    [GMP](https://gmplib.org/)); at runtime, `Nat` values that are sufficiently small are unboxed.
    
    Addition of natural numbers, typically used via the `+` operator.
    
    This function is overridden in both the kernel and the compiler to efficiently evaluate using the
    arbitrary-precision arithmetic library. The definition provided here is the logical model.
    
Lemma5.2
XL∃∀Nused by 0

Statement depends on Definition 5.1.

Theorem5.3
XL∃∀Nused by 0

Statement facet marker for preview relationships.

Proof

Proof facet marker for preview relationships, depending on Definition 5.1.

Theorem5.4
XL∃∀Nused by 0

Statement facet marker for preview relationships.

Proof

Proof facet marker for preview relationships.