logo

Expression of type Equals

from the theory of proveit.numbers.number_sets.integers

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import n
from proveit.logic import Equals, SetOfAll, Union
from proveit.numbers import Integer, Natural, NaturalPos, Neg
In [2]:
# build up the expression from sub-expressions
expr = Equals(Integer, Union(Natural, SetOfAll(instance_param_or_params = [n], instance_element = Neg(n), domain = NaturalPos)))
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{Z} = \left(\mathbb{N} \cup \left\{-n\right\}_{n \in \mathbb{N}^+}\right)
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
operands: 6
5Literal
6ExprTuple7, 8
7Literal
8Operationoperator: 9
operand: 11
9Literal
10ExprTuple11
11Lambdaparameter: 19
body: 12
12Conditionalvalue: 13
condition: 14
13Operationoperator: 15
operand: 19
14Operationoperator: 17
operands: 18
15Literal
16ExprTuple19
17Literal
18ExprTuple19, 20
19Variable
20Literal