# 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, 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 = ExprTuple(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(\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..\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
2ExprTuple29, 30, 24
3Conditionalvalue: 4
condition: 5
4Operationoperator: 19
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple9, 29
7Literal
8ExprTuple10, 11, 12, 13
9Operationoperator: 27
operands: 14
10Operationoperator: 17
operands: 15
11Operationoperator: 17
operands: 16
12Operationoperator: 17
operands: 18
13Operationoperator: 19
operands: 20
14ExprTuple24, 21
15ExprTuple29, 22
16ExprTuple30, 22
17Literal
18ExprTuple24, 22
19Literal
20ExprTuple23, 24
21Operationoperator: 25
operand: 30
22Literal
23Operationoperator: 27
operands: 28
24Variable
25Literal
26ExprTuple30
27Literal
28ExprTuple29, 30
29Variable
30Variable