{"id":"counter-sub-empty-means-containment","text":"`not (A - Counter(B))` is true iff B contains at least as many of every key as A; this Counter subtraction idiom (which drops zero/negative counts) is the sole correctness mechanism for the completing-word check.","truth_value":"IN","source":"entries/2026/06/06/shortest-completing-word-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":["counter-subtraction-is-multiset-containment-test"],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"counter-sub-empty-means-containment","truth_value":"IN","reason":"premise"}]}}