Theorem norm_triangle_ineq of type Forall

from the theory of proveit.linear_algebra.inner_products

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.linear_algebra.inner_products import norm_triangle_ineq

# check that the built expression is the same as the stored expression
assert norm_triangle_ineq.expr == stored_expr
assert norm_triangle_ineq.expr._style_id == stored_expr._style_id
print("Passed sanity check: norm_triangle_ineq matches stored_expr")

Passed sanity check: norm_triangle_ineq matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{K}~\left[\forall_{H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)}~\left[\forall_{x, y \in H}~\left(\left \|x + y\right \| \leq \left(\left \|x\right \| + \left \|y\right \|\right)\right)\right]\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 10 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 21 body: 3
3	Operation	operator: 10 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 39 body: 7
6	ExprTuple	39
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 14
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	39, 15
14	Lambda	parameters: 41 body: 16
15	Operation	operator: 17 operand: 21
16	Conditional	value: 19 condition: 20
17	Literal
18	ExprTuple	21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Variable
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 43 operand: 36
27	Operation	operator: 31 operands: 32
28	Operation	operator: 34 operands: 33
29	Operation	operator: 34 operands: 35
30	ExprTuple	36
31	Literal
32	ExprTuple	37, 38
33	ExprTuple	45, 39
34	Literal
35	ExprTuple	46, 39
36	Operation	operator: 40 operands: 41
37	Operation	operator: 43 operand: 45
38	Operation	operator: 43 operand: 46
39	Variable
40	Literal
41	ExprTuple	45, 46
42	ExprTuple	45
43	Literal
44	ExprTuple	46
45	Variable
46	Variable