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 H, K, Lambda, x
from proveit.linear_algebra import InnerProd, InnerProdSpaces, Norm
from proveit.logic import Equals, Forall
from proveit.numbers import sqrt

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

K \mapsto \left[\forall_{H \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(K\right)}~\left[\forall_{x \in H}~\left(\left \|x\right \| = \sqrt{\left \langle x, x\right \rangle}\right)\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: 19 body: 1
1	Operation	operator: 8 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 26 body: 5
4	ExprTuple	26
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 12
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	26, 13
12	Lambda	parameter: 37 body: 14
13	Operation	operator: 15 operand: 19
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	Variable
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	37, 26
24	Operation	operator: 27 operand: 37
25	Operation	operator: 29 operands: 30
26	Variable
27	Literal
28	ExprTuple	37
29	Literal
30	ExprTuple	31, 32
31	Operation	operator: 33 operands: 34
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	37, 37
35	Literal
36	ExprTuple	38, 39
37	Variable
38	Literal
39	Literal