# 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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import c
from proveit.core_expr_types import a_1_to_i, b_1_to_j, d_1_to_k
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Complex

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c, d_1_to_k], instance_expr = Equals(Add(a_1_to_i, b_1_to_j, c, d_1_to_k), Add(a_1_to_i, c, b_1_to_j, d_1_to_k)).with_wrapping_at(2), domain = Complex)

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())

\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c, d_{1}, d_{2}, \ldots, d_{k} \in \mathbb{C}}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ b_{1} +  b_{2} +  \ldots +  b_{j} + c+ d_{1} +  d_{2} +  \ldots +  d_{k}\right) =  \\ \left(a_{1} +  a_{2} +  \ldots +  a_{i} + c+ b_{1} +  b_{2} +  \ldots +  b_{j}+ d_{1} +  d_{2} +  \ldots +  d_{k}\right) \end{array} \end{array}\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 17
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple13, 14, 15, 16
11Operationoperator: 18
operands: 17
12Operationoperator: 18
operands: 19
13ExprRangelambda_map: 20
start_index: 36
end_index: 32
14ExprRangelambda_map: 21
start_index: 36
end_index: 34
15Operationoperator: 40
operands: 22
16ExprRangelambda_map: 23
start_index: 36
end_index: 37
17ExprTuple24, 25, 29, 26
18Literal
19ExprTuple24, 29, 25, 26
20Lambdaparameter: 50
body: 27
21Lambdaparameter: 50
body: 28
22ExprTuple29, 45
23Lambdaparameter: 50
body: 30
24ExprRangelambda_map: 31
start_index: 36
end_index: 32
25ExprRangelambda_map: 33
start_index: 36
end_index: 34
26ExprRangelambda_map: 35
start_index: 36
end_index: 37
27Operationoperator: 40
operands: 38
28Operationoperator: 40
operands: 39
29Variable
30Operationoperator: 40
operands: 41
31Lambdaparameter: 50
body: 42
32Variable
33Lambdaparameter: 50
body: 43
34Variable
35Lambdaparameter: 50
body: 44
36Literal
37Variable
38ExprTuple42, 45
39ExprTuple43, 45
40Literal
41ExprTuple44, 45
42IndexedVarvariable: 46
index: 50
43IndexedVarvariable: 47
index: 50
44IndexedVarvariable: 48
index: 50
45Literal
46Variable
47Variable
48Variable
49ExprTuple50
50Variable