# from the theory of proveit.numbers.addition.subtraction¶

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 Conditional, a, b
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, subtract, zero
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(subtract(a, b), zero), And(InSet(a, Complex), InSet(b, Complex), Equals(a, b)))
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(a - b\right) = 0 \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  a = b\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: 16
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 7
4Literal
5ExprTuple8, 9, 10
6Operationoperator: 11
operands: 12
7Literal
8Operationoperator: 14
operands: 13
9Operationoperator: 14
operands: 15
10Operationoperator: 16
operands: 17
11Literal
12ExprTuple20, 18
13ExprTuple20, 19
14Literal
15ExprTuple23, 19
16Literal
17ExprTuple20, 23
18Operationoperator: 21
operand: 23
19Literal
20Variable
21Literal
22ExprTuple23
23Variable