# from the theory of proveit.numbers.number_sets.rational_numbers¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import Expression classes needed to build the expression
from proveit import q
from proveit.logic import Equals, SetOfAll
from proveit.numbers import Rational, RationalNonNeg, greater_eq, zero

In [2]:
# build up the expression from sub-expressions
expr = Equals(RationalNonNeg, SetOfAll(instance_param_or_params = [q], instance_element = q, domain = Rational, condition = greater_eq(q, zero)))

expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\mathbb{Q}^{\geq 0} = \left\{q~|~q \geq 0\right\}_{q \in \mathbb{Q}}

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Literal
4Operationoperator: 5
operand: 7
5Literal
6ExprTuple7
7Lambdaparameter: 21
body: 9
8ExprTuple21
9Conditionalvalue: 21
condition: 10
10Operationoperator: 11
operands: 12
11Literal
12ExprTuple13, 14
13Operationoperator: 15
operands: 16
14Operationoperator: 17
operands: 18
15Literal
16ExprTuple21, 19
17Literal
18ExprTuple20, 21
19Literal
20Literal
21Variable