```typescript
export function mergeIntervals(intervals: number[][]): number[][] {
  if (!intervals.every(([start, end]) => start <= end)) {
    throw new Error("Invalid intervals: start must not be greater than end.");
  }

  const merged: number[][] = [];
  intervals.sort((a, b) => a[0] - b[0]);

  for (let i = 0; i < intervals.length; i++) {
    if (merged.length === 0 || merged[merged.length - 1][1] < intervals[i][0]) {
      merged.push(intervals[i]);
    } else {
      merged[merged.length - 1][1] = Math.max(merged[merged.length - 1][1], intervals[i][1]);
    }
  }

  return merged;
}
```