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Expression of type Equals

from the theory of proveit.numbers.summation

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 a, b, l
from proveit.logic import Equals
from proveit.numbers import Add, Integer, Mult, Sum, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = Mult(a, b)
sub_expr3 = Add(l, one)
expr = Equals(Sum(index_or_indices = sub_expr1, summand = Mult(sub_expr2, sub_expr3), domain = Integer), Mult(sub_expr2, Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = Integer)))
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[\sum_{l \in \mathbb{Z}}~\left(\left(a \cdot b\right) \cdot \left(l + 1\right)\right)\right] = \left(\left(a \cdot b\right) \cdot \left[\sum_{l \in \mathbb{Z}}~\left(l + 1\right)\right]\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 10
operand: 7
4Operationoperator: 20
operands: 6
5ExprTuple7
6ExprTuple17, 8
7Lambdaparameter: 29
body: 9
8Operationoperator: 10
operand: 13
9Conditionalvalue: 12
condition: 19
10Literal
11ExprTuple13
12Operationoperator: 20
operands: 14
13Lambdaparameter: 29
body: 16
14ExprTuple17, 18
15ExprTuple29
16Conditionalvalue: 18
condition: 19
17Operationoperator: 20
operands: 21
18Operationoperator: 22
operands: 23
19Operationoperator: 24
operands: 25
20Literal
21ExprTuple26, 27
22Literal
23ExprTuple29, 28
24Literal
25ExprTuple29, 30
26Variable
27Variable
28Literal
29Variable
30Literal