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, x
from proveit.linear_algebra import InnerProd, InnerProdSpaces, Norm
from proveit.logic import Equals, Forall, InClass
from proveit.numbers import sqrt

# build up the expression from sub-expressions
expr = Lambda(H, Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(Norm(x), sqrt(InnerProd(x, x))), 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())

H \mapsto \left\{\forall_{x \in H}~\left(\left \|x\right \| = \sqrt{\left \langle x, x\right \rangle}\right) \textrm{ if } H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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