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, K, x, y
from proveit.linear_algebra import InnerProdSpaces, Norm, VecAdd
from proveit.logic import Forall, InClass
from proveit.numbers import Add, LessEq

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x, y], instance_expr = LessEq(Norm(VecAdd(x, y)), Add(Norm(x), Norm(y))), domain = H), InClass(H, InnerProdSpaces(K)))

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\{\forall_{x, y \in H}~\left(\left \|x + y\right \| \leq \left(\left \|x\right \| + \left \|y\right \|\right)\right) \textrm{ if } H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)\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 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	32, 8
7	Lambda	parameters: 34 body: 9
8	Operation	operator: 10 operand: 14
9	Conditional	value: 12 condition: 13
10	Literal
11	ExprTuple	14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	Variable
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22
19	Operation	operator: 36 operand: 29
20	Operation	operator: 24 operands: 25
21	Operation	operator: 27 operands: 26
22	Operation	operator: 27 operands: 28
23	ExprTuple	29
24	Literal
25	ExprTuple	30, 31
26	ExprTuple	38, 32
27	Literal
28	ExprTuple	39, 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 36 operand: 38
31	Operation	operator: 36 operand: 39
32	Variable
33	Literal
34	ExprTuple	38, 39
35	ExprTuple	38
36	Literal
37	ExprTuple	39
38	Variable
39	Variable