Expression of type Equals

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 Conditional, fi, i, x, y, z
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, InSet
from proveit.numbers import Interval, four, two

# build up the expression from sub-expressions
sub_expr1 = TensorProd(x, TensorProd(y, fi), z)
expr = Equals(Conditional(sub_expr1, InSet(i, Interval(two, four))), sub_expr1)

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())

\left\{x {\otimes} \left(y {\otimes} f\left(i\right)\right) {\otimes} z \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right.. = \left(x {\otimes} \left(y {\otimes} f\left(i\right)\right) {\otimes} z\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

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