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Expression of type Conditional

from the theory of proveit.numbers.negation

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
from proveit.numbers import Complex, Mult, Neg
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(Mult(Neg(x), Neg(y)), Mult(x, y)), And(InSet(x, Complex), InSet(y, Complex)))
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\{\left(\left(-x\right) \cdot \left(-y\right)\right) = \left(x \cdot y\right) \textrm{ if } x \in \mathbb{C} ,  y \in \mathbb{C}\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
7Operationoperator: 12
operands: 11
8Operationoperator: 12
operands: 13
9Operationoperator: 15
operands: 14
10Operationoperator: 15
operands: 16
11ExprTuple17, 18
12Literal
13ExprTuple23, 24
14ExprTuple23, 19
15Literal
16ExprTuple24, 19
17Operationoperator: 21
operand: 23
18Operationoperator: 21
operand: 24
19Literal
20ExprTuple23
21Literal
22ExprTuple24
23Variable
24Variable