Expression of type Forall

from the theory of proveit.linear_algebra.tensors

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 i, x, y
from proveit.linear_algebra import TensorProd
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Interval, Real, four, three, two

# build up the expression from sub-expressions
sub_expr1 = CartExp(Real, three)
expr = Forall(instance_param_or_params = [i], instance_expr = InSet(TensorProd(x, y), TensorProd(sub_expr1, sub_expr1)), domain = Interval(two, four))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{i \in \{2~\ldotp \ldotp~4\}}~\left(\left(x {\otimes} y\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 13 body: 5
4	ExprTuple	13
5	Conditional	value: 6 condition: 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	Variable
14	Operation	operator: 18 operands: 19
15	ExprTuple	20, 21
16	Literal
17	ExprTuple	22, 22
18	Literal
19	ExprTuple	23, 24
20	Variable
21	Variable
22	Operation	operator: 25 operands: 26
23	Literal
24	Literal
25	Literal
26	ExprTuple	27, 28
27	Literal
28	Literal