# 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, ExprTuple, Lambda, 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 = ExprTuple(Lambda([a, b], 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) \mapsto \left\{\left(a - b\right) = 0 \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  a = b\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 19
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 18
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10, 11, 12
8Operationoperator: 13
operands: 14
9Literal
10Operationoperator: 16
operands: 15
11Operationoperator: 16
operands: 17
12Operationoperator: 18
operands: 19
13Literal
14ExprTuple22, 20
15ExprTuple22, 21
16Literal
17ExprTuple25, 21
18Literal
19ExprTuple22, 25
20Operationoperator: 23
operand: 25
21Literal
22Variable
23Literal
24ExprTuple25
25Variable