# 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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, a, b, c
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 = ExprTuple(Lambda([a, b, c], Conditional(Equals(subtract(b, c), Neg(a)), And(InSet(a, Complex), InSet(b, Complex), InSet(c, Complex), Equals(Add(a, b), c)))))

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, c\right) \mapsto \left\{\left(b - c\right) = \left(-a\right) \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  c \in \mathbb{C} ,  \left(a + b\right) = c\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: 2
body: 3
2ExprTuple31, 32, 30
3Conditionalvalue: 4
condition: 5
4Operationoperator: 21
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple9, 10
7Literal
8ExprTuple11, 12, 13, 14
9Operationoperator: 28
operands: 15
10Operationoperator: 26
operand: 31
11Operationoperator: 19
operands: 17
12Operationoperator: 19
operands: 18
13Operationoperator: 19
operands: 20
14Operationoperator: 21
operands: 22
15ExprTuple32, 23
16ExprTuple31
17ExprTuple31, 24
18ExprTuple32, 24
19Literal
20ExprTuple30, 24
21Literal
22ExprTuple25, 30
23Operationoperator: 26
operand: 30
24Literal
25Operationoperator: 28
operands: 29
26Literal
27ExprTuple30
28Literal
29ExprTuple31, 32
30Variable
31Variable
32Variable