# from the theory of proveit.numbers.addition¶

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, i, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Complex, Natural, zero

In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j], instance_expr = Equals(Add(a_1_to_i, zero, b_1_to_j), Add(a_1_to_i, b_1_to_j)), domain = Complex), And(InSet(i, Natural), InSet(j, Natural)))

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\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\left(\left(a_{1} +  a_{2} +  \ldots +  a_{i} + 0+ b_{1} +  b_{2} +  \ldots +  b_{j}\right) = \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ b_{1} +  b_{2} +  \ldots +  b_{j}\right)\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N}\right..

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 6
2Operationoperator: 17
operands: 5
3Literal
4ExprTuple6
5ExprTuple7, 8
6Lambdaparameters: 25
body: 9
7Operationoperator: 39
operands: 10
8Operationoperator: 39
operands: 11
9Conditionalvalue: 12
condition: 13
10ExprTuple34, 14
11ExprTuple37, 14
12Operationoperator: 15
operands: 16
13Operationoperator: 17
operands: 18
14Literal
15Literal
16ExprTuple19, 20
17Literal
18ExprTuple21, 22
19Operationoperator: 24
operands: 23
20Operationoperator: 24
operands: 25
21ExprRangelambda_map: 26
start_index: 36
end_index: 34
22ExprRangelambda_map: 27
start_index: 36
end_index: 37
23ExprTuple29, 28, 30
24Literal
25ExprTuple29, 30
26Lambdaparameter: 47
body: 31
27Lambdaparameter: 47
body: 32
28Literal
29ExprRangelambda_map: 33
start_index: 36
end_index: 34
30ExprRangelambda_map: 35
start_index: 36
end_index: 37
31Operationoperator: 39
operands: 38
32Operationoperator: 39
operands: 40
33Lambdaparameter: 47
body: 41
34Variable
35Lambdaparameter: 47
body: 42
36Literal
37Variable
38ExprTuple41, 43
39Literal
40ExprTuple42, 43
41IndexedVarvariable: 44
index: 47
42IndexedVarvariable: 45
index: 47
43Literal
44Variable
45Variable
46ExprTuple47
47Variable