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Expression of type Equals

from the theory of proveit.linear_algebra.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 Function, i, v, vi
from proveit.linear_algebra import VecSum
from proveit.logic import Equals
from proveit.numbers import Add, Interval, eight, one, seven, zero
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [i]
expr = Equals(VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(one, eight)), VecSum(index_or_indices = sub_expr1, summand = Function(v, [Add(i, one)]), domain = Interval(zero, seven)))
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_{i=1}^{8} v\left(i\right)\right) = \left(\sum_{i=0}^{7} v\left(i + 1\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: 31
body: 10
9Lambdaparameter: 31
body: 11
10Conditionalvalue: 12
condition: 13
11Conditionalvalue: 14
condition: 15
12Operationoperator: 18
operand: 31
13Operationoperator: 20
operands: 17
14Operationoperator: 18
operand: 23
15Operationoperator: 20
operands: 21
16ExprTuple31
17ExprTuple31, 22
18Variable
19ExprTuple23
20Literal
21ExprTuple31, 24
22Operationoperator: 28
operands: 25
23Operationoperator: 26
operands: 27
24Operationoperator: 28
operands: 29
25ExprTuple32, 30
26Literal
27ExprTuple31, 32
28Literal
29ExprTuple33, 34
30Literal
31Variable
32Literal
33Literal
34Literal