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 a, u, v, w, x, y, z
from proveit.linear_algebra import ScalarMult, TensorProd, VecAdd
from proveit.logic import CartExp, Equals, Implies, InSet
from proveit.numbers import Real, three

# build up the expression from sub-expressions
sub_expr1 = ScalarMult(a, v)
sub_expr2 = CartExp(Real, three)
sub_expr3 = TensorProd(u, sub_expr1, VecAdd(w, x, y), z)
expr = Implies(InSet(sub_expr3, TensorProd(sub_expr2, sub_expr2, sub_expr2, sub_expr2)), Equals(sub_expr3, VecAdd(TensorProd(u, sub_expr1, w, z), TensorProd(u, sub_expr1, x, z), TensorProd(u, sub_expr1, y, z))).with_wrapping_at(2)).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(u {\otimes} \left(a \cdot v\right) {\otimes} \left(w + x + y\right) {\otimes} z\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(u {\otimes} \left(a \cdot v\right) {\otimes} \left(w + x + y\right) {\otimes} z\right) =  \\ \left(\left(u {\otimes} \left(a \cdot v\right) {\otimes} w {\otimes} z\right) + \left(u {\otimes} \left(a \cdot v\right) {\otimes} x {\otimes} z\right) + \left(u {\otimes} \left(a \cdot v\right) {\otimes} y {\otimes} z\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: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	10, 9
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 26 operands: 12
10	Operation	operator: 26 operands: 13
11	Operation	operator: 22 operands: 14
12	ExprTuple	15, 15, 15, 15
13	ExprTuple	32, 33, 16, 35
14	ExprTuple	17, 18, 19
15	Operation	operator: 20 operands: 21
16	Operation	operator: 22 operands: 23
17	Operation	operator: 26 operands: 24
18	Operation	operator: 26 operands: 25
19	Operation	operator: 26 operands: 27
20	Literal
21	ExprTuple	28, 29
22	Literal
23	ExprTuple	30, 31, 34
24	ExprTuple	32, 33, 30, 35
25	ExprTuple	32, 33, 31, 35
26	Literal
27	ExprTuple	32, 33, 34, 35
28	Literal
29	Literal
30	Variable
31	Variable
32	Variable
33	Operation	operator: 36 operands: 37
34	Variable
35	Variable
36	Literal
37	ExprTuple	38, 39
38	Variable
39	Variable