| Symbol | Specification | Kind | Type |
|---|---|---|---|
| . * . | real-multdiv | f | Real × Real → Real |
| . + . | int-basic2 | f | Int × Int → Int |
| . + . | real-basic | f | Real × Real → Real |
| . + . | nat-basic | f | Nat × Nat → Nat |
| . +1 | int-basic1 | f | Int → Int |
| . +1 | nat-basic | f | Nat → Nat |
| . - . | int-abs | f | Int × Int → Int |
| . - . | real-abs | f | Real × Real → Real |
| . - . | nat | pf | Nat × Nat → Nat with λ n, m. n ≥ m |
| . -1 | int-basic1 | f | Int → Int |
| . -1 | nat-basic | pf | Nat → Nat with λ n. n ≠ 0 |
| . .r | real-basic | f | Int → Real |
| . / . | real-multdiv | pf | Real × Real → Real with λ r0, r. r ≠ 0.r |
| . < . | int-basic1 | p | Int × Int |
| . < . | real-basic | p | Real × Real |
| . < . | nat-basic | p | Nat × Nat |
| . > . | int-abs | p | Int × Int |
| . > . | real-abs | p | Real × Real |
| . > . | nat | p | Nat × Nat |
| . ^-1 | real-multdiv | pf | Real → Real with λ r. r ≠ 0.r |
| . ≤ . | int-abs | p | Int × Int |
| . ≤ . | real-abs | p | Real × Real |
| . ≤ . | real-supinf | p | (Real → Type(Bool)) × Real |
| . ≤ . | real-supinf | p | Real × (Real → Type(Bool)) |
| . ≤ . | nat | p | Nat × Nat |
| . ≥ . | int-abs | p | Int × Int |
| . ≥ . | real-abs | p | Real × Real |
| . ≥ . | nat | p | Nat × Nat |
| ~ . | int-abs | f | Int → Int |
| ~ . | real-basic | f | Real → Real |
| ε | real-limit | v | Real |
| Int | int-basic1 | s | |
| Nat | nat-basic | s | |
| Real | real-basic | s | |
| abs | int-abs | f | Int → Int |
| abs | real-abs | f | Real → Real |
| bounded≤ | real-supinf | p | (Real → Type(Bool)) |
| bounded≤ | real-limit | p | (Nat → Type(Real)) × Real |
| bounded≥ | real-supinf | p | (Real → Type(Bool)) |
| bounded≥ | real-limit | p | (Nat → Type(Real)) × Real |
| converges | real-limit | p | (Nat → Type(Real)) |
| converges | real-limit | p | (Nat → Type(Real)) × Real |
| f | real-limit | v | Nat → Real |
| i | real-limit | v | Int |
| inf | real-supinf | pf | (Real → Bool) → Real with λ rset. bounded≥(rset) |
| j | real-limit | v | Int |
| limit | real-limit | pf | (Nat → Real) → Real with λ f. converges(f) |
| max | real-min-max | f | Real × Real → Real |
| min | real-min-max | f | Real × Real → Real |
| mon≤ | real-limit | p | (Nat → Type(Real)) |
| mon≥ | real-limit | p | (Nat → Type(Real)) |
| n | real-limit | v | Nat |
| r | real-limit | v | Real |
| sup | real-supinf | pf | (Real → Bool) → Real with λ rset. bounded≤(rset) |