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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 VecAdd, VecSum
from proveit.logic import Equals
from proveit.numbers import Interval, eight, one, seven
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)), VecAdd(VecSum(index_or_indices = sub_expr1, summand = vi, domain = Interval(one, seven)), Function(v, [eight])))
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(\left(\sum_{i=1}^{7} v\left(i\right)\right) + v\left(8\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: 12
operand: 8
4Operationoperator: 6
operands: 7
5ExprTuple8
6Literal
7ExprTuple9, 10
8Lambdaparameter: 28
body: 11
9Operationoperator: 12
operand: 16
10Operationoperator: 23
operand: 27
11Conditionalvalue: 20
condition: 15
12Literal
13ExprTuple16
14ExprTuple27
15Operationoperator: 25
operands: 17
16Lambdaparameter: 28
body: 18
17ExprTuple28, 19
18Conditionalvalue: 20
condition: 21
19Operationoperator: 30
operands: 22
20Operationoperator: 23
operand: 28
21Operationoperator: 25
operands: 26
22ExprTuple32, 27
23Variable
24ExprTuple28
25Literal
26ExprTuple28, 29
27Literal
28Variable
29Operationoperator: 30
operands: 31
30Literal
31ExprTuple32, 33
32Literal
33Literal