lemmaly — Algorithm-First Proof

The model already knows Big-O, hash tables, divide-and-conquer, dynamic programming, sorting, graph algorithms, and amortized analysis. It just does not apply them spontaneously. lemmaly fixes the behavior, not the knowledge.

This skill is the gateway for an algorithm-discipline suite of four skills (lemmaly, mathguard, invariant-guard, complexity-cuts). It enforces the hard rules that every other guard in the suite assumes.

Violating the letter of these rules is violating the spirit of the skill. "Just this once" is how O(n²) ships to production.

When to Use This Skill

Use lemmaly when:

• Writing, editing, or reviewing code that involves loops, collections, lookups, searches, joins, recursion, graphs, queries, or any computation over more than a handful of items.
• About to write a for inside a for, .find / .includes / .indexOf inside a loop, await inside for / map / forEach over independent items, or one query per item in a collection.
• Auditing a codebase / PR for known anti-patterns (await-in-loop, .includes inside .filter, string-concat in loop, SELECT *, N+1, etc.).
• Reviewing AI-generated code that "looks idiomatic" but might hide O(n²) or N+1.

When in doubt, start at lemmaly — it is the gateway and will tell you when to escalate to its three sibling skills.