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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 k, n
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Mult, Sum, frac, one, two
In [2]:
# build up the expression from sub-expressions
expr = Equals(Sum(index_or_indices = [k], summand = k, domain = Interval(one, n)), frac(Mult(n, Add(n, one)), two))
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_{k = 1}^{n} k\right) = \frac{n \cdot \left(n + 1\right)}{2}
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: 5
operand: 9
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9
7Literal
8ExprTuple10, 11
9Lambdaparameter: 22
body: 13
10Operationoperator: 14
operands: 15
11Literal
12ExprTuple22
13Conditionalvalue: 22
condition: 16
14Literal
15ExprTuple27, 17
16Operationoperator: 18
operands: 19
17Operationoperator: 20
operands: 21
18Literal
19ExprTuple22, 23
20Literal
21ExprTuple27, 26
22Variable
23Operationoperator: 24
operands: 25
24Literal
25ExprTuple26, 27
26Literal
27Variable