| Symbol | Specification | Kind | Type |
|---|---|---|---|
| # . | nat-bag | f | nat-bag → nat |
| . + . | nat-basic | f | nat × nat → nat |
| . ++ . | nat-bag | f | nat-bag × nat → nat-bag |
| . +1 | nat-basic | f | nat → nat |
| . - . | nat | pf | nat × nat → nat with λ n, m. n ≥ m |
| . -- . | nat-bag | f | nat-bag × nat → nat-bag |
| . -1 | nat-basic | pf | nat → nat with λ n. n ≠ 0 |
| . .max | bag-max | f | nat-bag → nat |
| . < . | nat-basic | p | nat × nat |
| . > . | nat | p | nat × nat |
| . \ . | nat-bag | f | nat-bag × nat-bag → nat-bag |
| . ∈ . | nat-bag | p | nat × nat-bag |
| . ∪ . | nat-bag | f | nat-bag × nat-bag → nat-bag |
| . ≤ . | nat | p | nat × nat |
| . ≥ . | nat | p | nat × nat |
| . ⊆ . | nat-bag | p | nat-bag × nat-bag |
| { . } | nat-bag | f | nat → nat-bag |
| ∅ | nat-bag | c | nat-bag |
| bag | nat-bag | v | nat-bag |
| bag0 | nat-bag | v | nat-bag |
| bag1 | nat-bag | v | nat-bag |
| bag2 | nat-bag | v | nat-bag |
| count | nat-bag | f | nat × nat-bag → nat |
| m | nat-basic | v | nat |
| n | nat-basic | v | nat |
| n0 | nat-basic | v | nat |
| n1 | nat-basic | v | nat |
| n2 | nat-bag | v | nat |
| n3 | nat-bag | v | nat |
| n4 | nat-bag | v | nat |
| nat | nat-basic | s | |
| nat-bag | nat-bag | s | |
| unique-elems | bag-max | p | nat-bag |