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
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import CartExp, Equals, Implies, InSet
from proveit.numbers import Interval, Mult, Real, four, three, two

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