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Expression of type Forall

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 fi, i, j, k, x
from proveit.logic import Equals, Forall
from proveit.numbers import Integer, Interval, Mult, Sum
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(j, k)
expr = Forall(instance_param_or_params = [j, k], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = Mult(x, fi), domain = sub_expr2), Mult(x, Sum(index_or_indices = sub_expr1, summand = fi, domain = sub_expr2))), domain = Integer)
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())
\forall_{j, k \in \mathbb{Z}}~\left(\left(\sum_{i = j}^{k} \left(x \cdot f\left(i\right)\right)\right) = \left(x \cdot \left(\sum_{i = j}^{k} f\left(i\right)\right)\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 40
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple13, 14
11Operationoperator: 23
operand: 19
12Operationoperator: 27
operands: 16
13Operationoperator: 35
operands: 17
14Operationoperator: 35
operands: 18
15ExprTuple19
16ExprTuple30, 20
17ExprTuple41, 21
18ExprTuple42, 21
19Lambdaparameter: 37
body: 22
20Operationoperator: 23
operand: 26
21Literal
22Conditionalvalue: 25
condition: 32
23Literal
24ExprTuple26
25Operationoperator: 27
operands: 28
26Lambdaparameter: 37
body: 29
27Literal
28ExprTuple30, 31
29Conditionalvalue: 31
condition: 32
30Variable
31Operationoperator: 33
operand: 37
32Operationoperator: 35
operands: 36
33Variable
34ExprTuple37
35Literal
36ExprTuple37, 38
37Variable
38Operationoperator: 39
operands: 40
39Literal
40ExprTuple41, 42
41Variable
42Variable