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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, a, b
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Complex, Neg, subtract
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(Neg(subtract(a, b)), Add(Neg(a), b)), And(InSet(a, Complex), InSet(b, 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(a - b\right)\right) = \left(-a + b\right) \textrm{ if } a \in \mathbb{C} ,  b \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: 24
operand: 16
8Operationoperator: 19
operands: 12
9Operationoperator: 14
operands: 13
10Operationoperator: 14
operands: 15
11ExprTuple16
12ExprTuple17, 26
13ExprTuple23, 18
14Literal
15ExprTuple26, 18
16Operationoperator: 19
operands: 20
17Operationoperator: 24
operand: 23
18Literal
19Literal
20ExprTuple23, 22
21ExprTuple23
22Operationoperator: 24
operand: 26
23Variable
24Literal
25ExprTuple26
26Variable