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

In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, b, c], Conditional(Equals(subtract(c, b), 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(c - b\right) = a \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
1ExprTuple28, 29, 23
2Conditionalvalue: 3
condition: 4
3Operationoperator: 18
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 28
6Literal
7ExprTuple9, 10, 11, 12
8Operationoperator: 26
operands: 13
9Operationoperator: 16
operands: 14
10Operationoperator: 16
operands: 15
11Operationoperator: 16
operands: 17
12Operationoperator: 18
operands: 19
13ExprTuple23, 20
14ExprTuple28, 21
15ExprTuple29, 21
16Literal
17ExprTuple23, 21
18Literal
19ExprTuple22, 23
20Operationoperator: 24
operand: 29
21Literal
22Operationoperator: 26
operands: 27
23Variable
24Literal
25ExprTuple29
26Literal
27ExprTuple28, 29
28Variable
29Variable