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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, Qx, fx, x
from proveit.logic import Forall, InSet
from proveit.numbers import Real, Sum
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(fx, Real), condition = Qx), InSet(Sum(index_or_indices = sub_expr1, summand = fx, condition = Qx), Real))
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_{x~|~Q\left(x\right)}~\left(f\left(x\right) \in \mathbb{R}\right), \left[\sum_{x~|~Q\left(x\right)}~f\left(x\right)\right] \in \mathbb{R}\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: 13
operands: 5
3Literal
4ExprTuple6
5ExprTuple7, 16
6Lambdaparameter: 22
body: 8
7Operationoperator: 9
operand: 12
8Conditionalvalue: 11
condition: 18
9Literal
10ExprTuple12
11Operationoperator: 13
operands: 14
12Lambdaparameter: 22
body: 15
13Literal
14ExprTuple17, 16
15Conditionalvalue: 17
condition: 18
16Literal
17Operationoperator: 19
operand: 22
18Operationoperator: 20
operand: 22
19Variable
20Variable
21ExprTuple22
22Variable