External Markup Source Showcase

2. Bodyless Markdown statement with Lean declarations🔗

This theorem is not native Verso yet. The theorem directive intentionally has no body, but it still has source provenance, imported Markdown, and Lean declarations. The preview manifest must therefore keep the source and Lean data on the external-markup entry.

Theorem2.1
Original source
Source provenance preview
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Original source
  • Documentimported-paper
    imported-paper p. 12
    • page 12; text source/pages/page-12.md:4-15; pdf source/pages/page-12.pdf; image source/pages/images/page-12.png
uses 0
Used by 2
Reverse dependency previews
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Theorem 6.1
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markupMDL∃∀N

Rendered from external Markdown source (statement): source/pages/page-12.md:4:0-15:0; no native Verso body is available.

Theorem 2.1

For every natural number $n$, the imported source states that addition and multiplication have canonical recursive behavior.

  • Source text is Markdown, not Verso.
  • The Blueprint node is intentionally bodyless.
  • Lean declarations are still attached to the manifest entry.
Lean code for Theorem2.12 definitions
  • defdefined in Init/Prelude.lean
    complete
    def Nat.add : Nat  Nat  Nat
    def Nat.add : Nat  Nat  Nat
    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.
    
  • defdefined in Init/Prelude.lean
    complete
    def Nat.mul : Nat  Nat  Nat
    def Nat.mul : Nat  Nat  Nat
    Multiplication of natural numbers, usually accessed 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.