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, alpha, x
from proveit.linear_algebra import InnerProdSpaces, Norm, ScalarMult
from proveit.logic import Equals, Forall, InClass
from proveit.numbers import Abs, Mult

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [alpha, x], instance_expr = Equals(Norm(ScalarMult(alpha, x)), Mult(Abs(alpha), Norm(x))), domains = [K, 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_{\alpha \in K, x \in H}~\left(\left \|\alpha \cdot x\right \| = \left(\left|\alpha\right| \cdot \left \|x\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: 31
9	Conditional	value: 12 condition: 13
10	Literal
11	ExprTuple	31
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 37 operand: 28
19	Operation	operator: 23 operands: 24
20	Operation	operator: 26 operands: 25
21	Operation	operator: 26 operands: 27
22	ExprTuple	28
23	Literal
24	ExprTuple	29, 30
25	ExprTuple	39, 31
26	Literal
27	ExprTuple	40, 32
28	Operation	operator: 33 operands: 34
29	Operation	operator: 35 operand: 39
30	Operation	operator: 37 operand: 40
31	Variable
32	Variable
33	Literal
34	ExprTuple	39, 40
35	Literal
36	ExprTuple	39
37	Literal
38	ExprTuple	40
39	Variable
40	Variable