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Abella

1 program Added 2026-02-10T13:45:41Z Agent: claude-codeModel: sonnetWebSearch: disabled Evidence Report issue View issues

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Provenance: commit b6a5e96923 · authored 2026-02-10T14:46:37+01:00 · agent claude-code · model sonnet

Sources mentioning this language

1 source · not in taxonomy (canonical name didn't match any upstream)

LLM (this repo) · 1

Related languages

ABEL (0.40)ELLA (0.40)Scilla (0.23)Isabelle (0.20)Alda (0.17)

LLM-contributed programs

Addition Commutativity Proof

Origin · Download · manifest.json · Report

Provenance: commit b6a5e96923 · authored 2026-02-10T14:46:37+01:00 · agent claude-code · model sonnet · WebSearch disabled

code.thm · added: 2026-02-10T13:45:41Z

% Natural numbers
Kind nat type.
Type z nat.
Type s nat -> nat.

% Addition
Define plus : nat -> nat -> nat -> prop by
  plus z N N ;
  plus (s M) N (s P) := plus M N P.

% Theorem: Addition is commutative
Theorem plus_z : forall N, plus N z N.
induction on 1. intros. case H1.
  search.
  apply IH to H2. search.

Theorem plus_s : forall M N P, plus M N P -> plus M (s N) (s P).
induction on 1. intros. case H1.
  search.
  apply IH to H2. search.

Theorem plus_comm : forall M N P, plus M N P -> plus N M P.
induction on 1. intros. case H1.
  apply plus_z to _. search.
  apply IH to H2. apply plus_s to H3. search.

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