feat: add independence of the parallel postulate eval problem#271
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This PR adds the independence of Euclid's parallel postulate (theorem #12 on Freek Wiedijk's "Formalizing 100 Theorems" list) as a new eval problem. It uses Tarski's axiomatization: a `TarskiAbsolute` class bundling the betweenness and congruence primitives with axioms A1-A9 and the continuity axiom A11, the Euclidean axiom A10 as a separate `Prop`, and independence stated as the conjunction of two existentials. The statement was cross-checked against the HOL Light (Harrison) and Isabelle (Makarios) formalizations recorded on Freek's list. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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This PR adds the independence of Euclid's parallel postulate as a new lean-eval challenge problem — theorem #12 on Freek Wiedijk's Formalizing 100 Theorems list, which currently has no Lean formalization.
The problem uses Tarski's axiomatization.
TarskiAbsolutebundles the betweenness (B) and congruence (C) primitives with axioms A1-A9 and the continuity axiom A11 — everything except the parallel postulate. The Euclidean axiom A10 is a separateProp, andparallel_postulate_independentasserts both that some model satisfies A10 (the real coordinate plane) and that some model refutes it (the Klein-Beltrami disk model of the hyperbolic plane).The formal statement was cross-checked against the two existing formalizations recorded on Freek's list:
Multivariate/tarski.ml+100/independence.mlTarskis_Geometry(from his 2012 MSc thesis)Axioms A1-A10 match Harrison's
TARSKI_AXIOM_ncharacter-for-character; A11 is his second-order continuity axiom. Both reference formalizations verify A1-A9 and A11 for the Klein model, so including A11 makes this the full-strength independence theorem rather than the weaker independence from A1-A9 alone.🤖 Prepared with Claude Code