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Expression of type ExprTuple

from the theory of proveit.linear_algebra.tensors

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, i, x
from proveit.linear_algebra import VecSum
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Interval, Real, four, three, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = CartExp(Real, three)
sub_expr3 = Interval(two, four)
expr = ExprTuple(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(x, sub_expr2), domain = sub_expr3), InSet(VecSum(index_or_indices = sub_expr1, summand = x, domain = sub_expr3), sub_expr2))
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_{i \in \{2~\ldotp \ldotp~4\}}~\left(x \in \mathbb{R}^{3}\right), \left(\sum_{i=2}^{4} x\right) \in \mathbb{R}^{3}\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: 21
operands: 5
3Literal
4ExprTuple6
5ExprTuple7, 16
6Lambdaparameter: 25
body: 8
7Operationoperator: 9
operand: 12
8Conditionalvalue: 11
condition: 18
9Literal
10ExprTuple12
11Operationoperator: 21
operands: 13
12Lambdaparameter: 25
body: 15
13ExprTuple17, 16
14ExprTuple25
15Conditionalvalue: 17
condition: 18
16Operationoperator: 19
operands: 20
17Variable
18Operationoperator: 21
operands: 22
19Literal
20ExprTuple23, 24
21Literal
22ExprTuple25, 26
23Literal
24Literal
25Variable
26Operationoperator: 27
operands: 28
27Literal
28ExprTuple29, 30
29Literal
30Literal