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feat(untyped): the Leftmost Reduction Theorem#700

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m-ow wants to merge 10 commits into
leanprover:mainfrom
m-ow:leftmost-reduction
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feat(untyped): the Leftmost Reduction Theorem#700
m-ow wants to merge 10 commits into
leanprover:mainfrom
m-ow:leftmost-reduction

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@m-ow

@m-ow m-ow commented Jul 8, 2026

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Introduces leftmost reduction ⭢ℓ, a beta-step contracting the redex at position 0, together with normal forms, and proves the Leftmost Reduction Theorem: if a term beta-reduces to a normal form, the leftmost strategy reaches it too.
The result falls out of standardization, following Copes (2018).

Builds on top of #679

@lengyijun

lengyijun commented Jul 8, 2026

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Can you add 2 theorems :

  1. NormalForm M <-> Normal FullBeta M
  2. Decidable Normal FullBeta

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3 participants