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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 a, b, c, i, vi
from proveit.linear_algebra import VecAdd, VecSum
from proveit.logic import Equals
from proveit.numbers import Add, Interval, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [i]
expr = Equals(VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(a, c)), VecAdd(VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(a, b)), VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(Add(b, one), c))))
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=a}^{c} v\left(i\right)\right) = \left(\left(\sum_{i=a}^{b} v\left(i\right)\right) + \left(\sum_{i=b + 1}^{c} v\left(i\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: 13
operand: 8
4Operationoperator: 6
operands: 7
5ExprTuple8
6Literal
7ExprTuple9, 10
8Lambdaparameter: 32
body: 11
9Operationoperator: 13
operand: 16
10Operationoperator: 13
operand: 17
11Conditionalvalue: 23
condition: 15
12ExprTuple16
13Literal
14ExprTuple17
15Operationoperator: 29
operands: 18
16Lambdaparameter: 32
body: 19
17Lambdaparameter: 32
body: 20
18ExprTuple32, 21
19Conditionalvalue: 23
condition: 22
20Conditionalvalue: 23
condition: 24
21Operationoperator: 35
operands: 25
22Operationoperator: 29
operands: 26
23Operationoperator: 27
operand: 32
24Operationoperator: 29
operands: 30
25ExprTuple37, 39
26ExprTuple32, 31
27Variable
28ExprTuple32
29Literal
30ExprTuple32, 33
31Operationoperator: 35
operands: 34
32Variable
33Operationoperator: 35
operands: 36
34ExprTuple37, 42
35Literal
36ExprTuple38, 39
37Variable
38Operationoperator: 40
operands: 41
39Variable
40Literal
41ExprTuple42, 43
42Variable
43Literal