Expression of type Lambda

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, Lambda, alpha, x
from proveit.linear_algebra import Norm, ScalarMult
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, Mult

# build up the expression from sub-expressions
expr = Lambda([alpha, x], Conditional(Equals(Norm(ScalarMult(alpha, x)), Mult(Abs(alpha), Norm(x))), And(InSet(alpha, K), InSet(x, 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(\alpha, x\right) \mapsto \left\{\left \|\alpha \cdot x\right \| = \left(\left|\alpha\right| \cdot \left \|x\right \|\right) \textrm{ if } \alpha \in K ,  x \in H\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 24 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 27 operand: 18
9	Operation	operator: 13 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	18
13	Literal
14	ExprTuple	19, 20
15	ExprTuple	29, 21
16	Literal
17	ExprTuple	30, 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 25 operand: 29
20	Operation	operator: 27 operand: 30
21	Variable
22	Variable
23	Literal
24	ExprTuple	29, 30
25	Literal
26	ExprTuple	29
27	Literal
28	ExprTuple	30
29	Variable
30	Variable