# 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, Lambda, a, b, c
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Complex, Neg

In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, b, c], Conditional(Equals(Add(c, Neg(a), b), c), And(InSet(a, Complex), InSet(b, Complex), InSet(c, 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(a, b, c\right) \mapsto \left\{\left(c - a + b\right) = c \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  c \in \mathbb{C} ,  a = b\right..

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple27, 24, 22
2Conditionalvalue: 3
condition: 4
3Operationoperator: 19
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 22
6Literal
7ExprTuple9, 10, 11, 12
8Operationoperator: 13
operands: 14
9Operationoperator: 17
operands: 15
10Operationoperator: 17
operands: 16
11Operationoperator: 17
operands: 18
12Operationoperator: 19
operands: 20
13Literal
14ExprTuple22, 21, 24
15ExprTuple27, 23
16ExprTuple24, 23
17Literal
18ExprTuple22, 23
19Literal
20ExprTuple27, 24
21Operationoperator: 25
operand: 27
22Variable
23Literal
24Variable
25Literal
26ExprTuple27
27Variable