Proof for mathd_algebra_513 - #46
Open
aleph-prover-test[bot] wants to merge 1 commit into
Open
Conversation
Automated commit at 20260127_160628
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Proven lemmas: 1/1
The goal is to prove that if real numbers a and b satisfy the linear system 3·a + 2·b = 5 and a + b = 2, then necessarily a = 1 and b = 1 (i.e., the unique solution is (1,1)). The proof is decomposed into two sub-goals: first derive ha : a = 1 from the two given equations, and then derive hb : b = 1 from the same equations. Both sub-goals have been solved: Lean uses the linarith tactic to eliminate variables and conclude each equality directly from h₀ and h₁. With ha and hb established, the final step bundles them into the conjunction a = 1 ∧ b = 1. So progress is complete: 2 out of 2 key sub-results are proven, and nothing remains. An interesting aspect is that while the system can be solved manually by simple elimination (e.g., subtracting 2·(a+b)=4 from 3a+2b=5 to get a=1), linarith automates this linear reasoning cleanly.