# 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 a, b
from proveit.logic import Equals, NotEquals, SetOfAll
from proveit.numbers import Integer, Rational, frac, zero

In [2]:
# build up the expression from sub-expressions
expr = Equals(Rational, SetOfAll(instance_param_or_params = [a, b], instance_element = frac(a, b), domain = Integer, condition = NotEquals(b, 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} = \left\{\frac{a}{b}~|~b \neq 0\right\}_{a, b \in \mathbb{Z}}

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
7Lambdaparameters: 12
body: 8
8Conditionalvalue: 9
condition: 10
9Operationoperator: 11
operands: 12
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple23, 25
13Literal
14ExprTuple15, 16, 17
15Operationoperator: 19
operands: 18
16Operationoperator: 19
operands: 20
17Operationoperator: 21
operands: 22
18ExprTuple23, 24
19Literal
20ExprTuple25, 24
21Literal
22ExprTuple25, 26
23Variable
24Literal
25Variable
26Literal