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, beta, gamma, i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Interval, four, one, two

# build up the expression from sub-expressions
sub_expr1 = ScalarMult(gamma, ScalarMult(i, ScalarMult(beta, ScalarMult(Add(i, one), TensorProd(x, y)))))
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\{\gamma \cdot \left(i \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\right)\right)\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right.. = \left(\gamma \cdot \left(i \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\right)\right)\right)\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: 21 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	29, 11
9	Variable
10	Operation	operator: 21 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	29, 15
13	Literal
14	ExprTuple	16, 17
15	Operation	operator: 21 operands: 18
16	Literal
17	Literal
18	ExprTuple	19, 20
19	Variable
20	Operation	operator: 21 operands: 22
21	Literal
22	ExprTuple	23, 24
23	Operation	operator: 25 operands: 26
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	31, 32
29	Variable
30	Literal
31	Variable
32	Variable