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Expression of type ExprTuple

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 ExprTuple, Function, f, g, k, l, m, n
from proveit.logic import Equals, Forall
from proveit.numbers import Interval, Sum
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = [l]
sub_expr3 = Interval(m, n)
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Function(f, sub_expr1), Function(g, sub_expr1)), domain = sub_expr3), Equals(Sum(index_or_indices = sub_expr2, summand = Function(f, sub_expr2), domain = sub_expr3), Sum(index_or_indices = sub_expr2, summand = Function(g, sub_expr2), domain = sub_expr3)))
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(\forall_{k \in \{m~\ldotp \ldotp~n\}}~\left(f\left(k\right) = g\left(k\right)\right), \left(\sum_{l = m}^{n} f\left(l\right)\right) = \left(\sum_{l = m}^{n} g\left(l\right)\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 3
operand: 6
2Operationoperator: 17
operands: 5
3Literal
4ExprTuple6
5ExprTuple7, 8
6Lambdaparameter: 33
body: 9
7Operationoperator: 11
operand: 15
8Operationoperator: 11
operand: 16
9Conditionalvalue: 13
condition: 14
10ExprTuple15
11Literal
12ExprTuple16
13Operationoperator: 17
operands: 18
14Operationoperator: 31
operands: 19
15Lambdaparameter: 34
body: 20
16Lambdaparameter: 34
body: 21
17Literal
18ExprTuple22, 23
19ExprTuple33, 35
20Conditionalvalue: 24
condition: 26
21Conditionalvalue: 25
condition: 26
22Operationoperator: 28
operand: 33
23Operationoperator: 29
operand: 33
24Operationoperator: 28
operand: 34
25Operationoperator: 29
operand: 34
26Operationoperator: 31
operands: 32
27ExprTuple33
28Variable
29Variable
30ExprTuple34
31Literal
32ExprTuple34, 35
33Variable
34Variable
35Operationoperator: 36
operands: 37
36Literal
37ExprTuple38, 39
38Variable
39Variable