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

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = TensorProd(x, y)
sub_expr3 = Interval(two, four)
sub_expr4 = CartExp(Real, three)
sub_expr5 = Mult(gamma, beta)
sub_expr6 = Mult(i, Add(i, one))
sub_expr7 = VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr6, sub_expr2), domain = sub_expr3)
expr = Implies(InSet(sub_expr7, TensorProd(sub_expr4, sub_expr4)), Equals(ScalarMult(sub_expr5, sub_expr7), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Mult(sub_expr5, sub_expr6), sub_expr2), domain = sub_expr3)).with_wrapping_at(1)).with_wrapping_at(1)

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(\left(i \cdot \left(i + 1\right)\right) \cdot \left(x {\otimes} y\right)\right)\right) \in \left(\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(\left(i \cdot \left(i + 1\right)\right) \cdot \left(x {\otimes} y\right)\right)\right)\right) \\  = \left(\sum_{i=2}^{4} \left(\left(\left(\gamma \cdot \beta\right) \cdot \left(i \cdot \left(i + 1\right)\right)\right) \cdot \left(x {\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.	()	(1)	('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: 34 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	15, 8
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 41 operands: 11
9	Operation	operator: 32 operands: 12
10	Operation	operator: 19 operand: 16
11	ExprTuple	14, 14
12	ExprTuple	39, 15
13	ExprTuple	16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operand: 24
16	Lambda	parameter: 57 body: 21
17	Literal
18	ExprTuple	22, 23
19	Literal
20	ExprTuple	24
21	Conditional	value: 25 condition: 30
22	Literal
23	Literal
24	Lambda	parameter: 57 body: 27
25	Operation	operator: 32 operands: 28
26	ExprTuple	57
27	Conditional	value: 29 condition: 30
28	ExprTuple	31, 37
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 46 operands: 36
32	Literal
33	ExprTuple	40, 37
34	Literal
35	ExprTuple	57, 38
36	ExprTuple	39, 40
37	Operation	operator: 41 operands: 42
38	Operation	operator: 43 operands: 44
39	Operation	operator: 46 operands: 45
40	Operation	operator: 46 operands: 47
41	Literal
42	ExprTuple	48, 49
43	Literal
44	ExprTuple	50, 51
45	ExprTuple	52, 53
46	Literal
47	ExprTuple	57, 54
48	Variable
49	Variable
50	Literal
51	Literal
52	Variable
53	Variable
54	Operation	operator: 55 operands: 56
55	Literal
56	ExprTuple	57, 58
57	Variable
58	Literal