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, Lambda, 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 = InSet(i, Interval(two, four))
sub_expr2 = ScalarMult(beta, ScalarMult(Add(i, one), TensorProd(x, y)))
expr = Equals(Lambda(i, Conditional(ScalarMult(gamma, ScalarMult(i, sub_expr2)), sub_expr1)), Lambda(i, Conditional(ScalarMult(ScalarMult(gamma, i), sub_expr2), sub_expr1))).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \left[i \mapsto \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..\right] =  \\ \left[i \mapsto \left\{\left(\gamma \cdot i\right) \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\right)\right) \textrm{ if } i \in \{2~\ldotp \ldotp~4\}\right..\right] \end{array} \end{array}

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.	()	(2)	('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	Lambda	parameter: 37 body: 5
4	Lambda	parameter: 37 body: 7
5	Conditional	value: 8 condition: 10
6	ExprTuple	37
7	Conditional	value: 9 condition: 10
8	Operation	operator: 29 operands: 11
9	Operation	operator: 29 operands: 12
10	Operation	operator: 13 operands: 14
11	ExprTuple	23, 15
12	ExprTuple	16, 22
13	Literal
14	ExprTuple	37, 17
15	Operation	operator: 29 operands: 18
16	Operation	operator: 29 operands: 19
17	Operation	operator: 20 operands: 21
18	ExprTuple	37, 22
19	ExprTuple	23, 37
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 29 operands: 26
23	Variable
24	Literal
25	Literal
26	ExprTuple	27, 28
27	Variable
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	Operation	operator: 33 operands: 34
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	39, 40
37	Variable
38	Literal
39	Variable
40	Variable