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Expression of type Conditional

from the theory of proveit.numbers.division

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 Conditional, x, y
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Neg, frac, zero
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(frac(x, Neg(y)), Neg(frac(x, y))), And(InSet(x, Complex), InSet(y, Complex), NotEquals(y, 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())
\left\{\frac{x}{-y} = \left(-\frac{x}{y}\right) \textrm{ if } x \in \mathbb{C} ,  y \in \mathbb{C} ,  y \neq 0\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple9, 10, 11
7Operationoperator: 25
operands: 12
8Operationoperator: 23
operand: 20
9Operationoperator: 15
operands: 14
10Operationoperator: 15
operands: 16
11Operationoperator: 17
operands: 18
12ExprTuple27, 19
13ExprTuple20
14ExprTuple27, 21
15Literal
16ExprTuple28, 21
17Literal
18ExprTuple28, 22
19Operationoperator: 23
operand: 28
20Operationoperator: 25
operands: 26
21Literal
22Literal
23Literal
24ExprTuple28
25Literal
26ExprTuple27, 28
27Variable
28Variable