Expression of type Conditional

from the theory of proveit.linear_algebra.inner_products

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 Conditional, H, x, y
from proveit.linear_algebra import Norm, VecAdd
from proveit.logic import And, InSet
from proveit.numbers import Add, LessEq

# build up the expression from sub-expressions
expr = Conditional(LessEq(Norm(VecAdd(x, y)), Add(Norm(x), Norm(y))), And(InSet(x, H), InSet(y, H)))

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\{\left \|x + y\right \| \leq \left(\left \|x\right \| + \left \|y\right \|\right) \textrm{ if } x \in H ,  y \in H\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 24 operand: 17
8	Operation	operator: 12 operands: 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprTuple	17
12	Literal
13	ExprTuple	18, 19
14	ExprTuple	26, 20
15	Literal
16	ExprTuple	27, 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 24 operand: 26
19	Operation	operator: 24 operand: 27
20	Variable
21	Literal
22	ExprTuple	26, 27
23	ExprTuple	26
24	Literal
25	ExprTuple	27
26	Variable
27	Variable