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 i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.logic import CartExp, Forall, 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 = CartExp(Real, three)
sub_expr3 = Interval(two, four)
sub_expr4 = TensorProd(sub_expr2, sub_expr2)
sub_expr5 = ScalarMult(Mult(i, Add(i, one)), TensorProd(x, y))
expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(sub_expr5, sub_expr4), domain = sub_expr3), InSet(VecSum(index_or_indices = sub_expr1, summand = sub_expr5, domain = sub_expr3), sub_expr4)).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[\forall_{i \in \{2~\ldotp \ldotp~4\}}~\left(\left(\left(i \cdot \left(i + 1\right)\right) \cdot \left(x {\otimes} y\right)\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)\right)\right] \Rightarrow  \\ \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) \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 operand: 8
4	Operation	operator: 24 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 18
8	Lambda	parameter: 47 body: 10
9	Operation	operator: 11 operand: 14
10	Conditional	value: 13 condition: 20
11	Literal
12	ExprTuple	14
13	Operation	operator: 24 operands: 15
14	Lambda	parameter: 47 body: 17
15	ExprTuple	19, 18
16	ExprTuple	47
17	Conditional	value: 19 condition: 20
18	Operation	operator: 34 operands: 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	ExprTuple	26, 26
22	Literal
23	ExprTuple	27, 28
24	Literal
25	ExprTuple	47, 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operands: 33
28	Operation	operator: 34 operands: 35
29	Operation	operator: 36 operands: 37
30	Literal
31	ExprTuple	38, 39
32	Literal
33	ExprTuple	47, 40
34	Literal
35	ExprTuple	41, 42
36	Literal
37	ExprTuple	43, 44
38	Literal
39	Literal
40	Operation	operator: 45 operands: 46
41	Variable
42	Variable
43	Literal
44	Literal
45	Literal
46	ExprTuple	47, 48
47	Variable
48	Literal