Expression of type Equals

from the theory of proveit.linear_algebra.addition

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, b
from proveit.linear_algebra import Norm, VecAdd
from proveit.logic import Equals
from proveit.numbers import Add, Exp, sqrt, two

# build up the expression from sub-expressions
expr = Equals(Norm(VecAdd(a, b)), sqrt(Add(Exp(Norm(a), two), Exp(Norm(b), two))))

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())

\left \|a + b\right \| = \sqrt{\left(\left \|a\right \|^{2} + \left \|b\right \|^{2}\right)}

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.	()	()	('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: 26 operand: 7
4	Operation	operator: 20 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operands: 15
10	Literal
11	ExprTuple	28, 29
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 24
16	Operation	operator: 20 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 24
20	Literal
21	ExprTuple	23, 24
22	Operation	operator: 26 operand: 28
23	Operation	operator: 26 operand: 29
24	Literal
25	ExprTuple	28
26	Literal
27	ExprTuple	29
28	Variable
29	Variable