Expression of type Implies

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 beta, fi, gamma, i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.logic import CartExp, Equals, Implies, InSet
from proveit.numbers import Interval, Real, four, three, two

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(two, four)
sub_expr3 = CartExp(Real, three)
sub_expr4 = ScalarMult(gamma, beta)
sub_expr5 = TensorProd(x, fi, y)
sub_expr6 = VecSum(index_or_indices = sub_expr1, summand = sub_expr5, domain = sub_expr2)
expr = Implies(InSet(sub_expr6, TensorProd(sub_expr3, sub_expr3, sub_expr3)), Equals(ScalarMult(sub_expr4, sub_expr6), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr4, sub_expr5), domain = sub_expr2)).with_wrapping_at(1)).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(\left(\sum_{i=2}^{4} \left(x {\otimes} f\left(i\right) {\otimes} y\right)\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(\left(\gamma \cdot \beta\right) \cdot \left(\sum_{i=2}^{4} \left(x {\otimes} f\left(i\right) {\otimes} y\right)\right)\right) \\  = \left(\sum_{i=2}^{4} \left(\left(\gamma \cdot \beta\right) \cdot \left(x {\otimes} f\left(i\right) {\otimes} y\right)\right)\right) \end{array} \end{array}\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	Operation	operator: 31 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	15, 8
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 35 operands: 11
9	Operation	operator: 33 operands: 12
10	Operation	operator: 19 operand: 16
11	ExprTuple	14, 14, 14
12	ExprTuple	29, 15
13	ExprTuple	16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operand: 24
16	Lambda	parameter: 49 body: 21
17	Literal
18	ExprTuple	22, 23
19	Literal
20	ExprTuple	24
21	Conditional	value: 25 condition: 28
22	Literal
23	Literal
24	Lambda	parameter: 49 body: 26
25	Operation	operator: 33 operands: 27
26	Conditional	value: 30 condition: 28
27	ExprTuple	29, 30
28	Operation	operator: 31 operands: 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 35 operands: 36
31	Literal
32	ExprTuple	49, 37
33	Literal
34	ExprTuple	38, 39
35	Literal
36	ExprTuple	40, 41, 42
37	Operation	operator: 43 operands: 44
38	Variable
39	Variable
40	Variable
41	Operation	operator: 45 operand: 49
42	Variable
43	Literal
44	ExprTuple	47, 48
45	Variable
46	ExprTuple	49
47	Literal
48	Literal
49	Variable