# 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, subtract

In [2]:
# build up the expression from sub-expressions
expr = 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(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..

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
1ExprTuple30, 31, 29
2Conditionalvalue: 3
condition: 4
3Operationoperator: 20
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10, 11, 12, 13
8Operationoperator: 27
operands: 14
9Operationoperator: 25
operand: 30
10Operationoperator: 18
operands: 16
11Operationoperator: 18
operands: 17
12Operationoperator: 18
operands: 19
13Operationoperator: 20
operands: 21
14ExprTuple31, 22
15ExprTuple30
16ExprTuple30, 23
17ExprTuple31, 23
18Literal
19ExprTuple29, 23
20Literal
21ExprTuple24, 29
22Operationoperator: 25
operand: 29
23Literal
24Operationoperator: 27
operands: 28
25Literal
26ExprTuple29
27Literal
28ExprTuple30, 31
29Variable
30Variable
31Variable