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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 Function, f, g, l, m, n
from proveit.logic import Equals
from proveit.numbers import Interval, Sum
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = Interval(m, n)
expr = Equals(Sum(index_or_indices = sub_expr1, summand = Function(f, sub_expr1), domain = sub_expr2), Sum(index_or_indices = sub_expr1, summand = Function(g, sub_expr1), domain = sub_expr2))
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 = m}^{n} f\left(l\right)\right) = \left(\sum_{l = m}^{n} g\left(l\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: 6
operand: 8
4Operationoperator: 6
operand: 9
5ExprTuple8
6Literal
7ExprTuple9
8Lambdaparameter: 20
body: 10
9Lambdaparameter: 20
body: 11
10Conditionalvalue: 12
condition: 14
11Conditionalvalue: 13
condition: 14
12Operationoperator: 15
operand: 20
13Operationoperator: 16
operand: 20
14Operationoperator: 18
operands: 19
15Variable
16Variable
17ExprTuple20
18Literal
19ExprTuple20, 21
20Variable
21Operationoperator: 22
operands: 23
22Literal
23ExprTuple24, 25
24Variable
25Variable