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

# build up the expression from sub-expressions
expr = Lambda(K, Forall(instance_param_or_params = [H], instance_expr = Forall(instance_param_or_params = [alpha, x], instance_expr = Equals(Norm(ScalarMult(alpha, x)), Mult(Abs(alpha), Norm(x))), domains = [K, 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_{\alpha \in K, x \in H}~\left(\left \|\alpha \cdot x\right \| = \left(\left|\alpha\right| \cdot \left \|x\right \|\right)\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: 36 body: 1
1	Operation	operator: 8 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 37 body: 5
4	ExprTuple	37
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	37, 13
12	Lambda	parameters: 39 body: 14
13	Operation	operator: 15 operand: 36
14	Conditional	value: 17 condition: 18
15	Literal
16	ExprTuple	36
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 42 operand: 33
24	Operation	operator: 28 operands: 29
25	Operation	operator: 31 operands: 30
26	Operation	operator: 31 operands: 32
27	ExprTuple	33
28	Literal
29	ExprTuple	34, 35
30	ExprTuple	44, 36
31	Literal
32	ExprTuple	45, 37
33	Operation	operator: 38 operands: 39
34	Operation	operator: 40 operand: 44
35	Operation	operator: 42 operand: 45
36	Variable
37	Variable
38	Literal
39	ExprTuple	44, 45
40	Literal
41	ExprTuple	44
42	Literal
43	ExprTuple	45
44	Variable
45	Variable