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

# build up the expression from sub-expressions
expr = Lambda(H, 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())

H \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 34 body: 2
1	ExprTuple	34
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	34, 10
9	Lambda	parameters: 36 body: 11
10	Operation	operator: 12 operand: 33
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	33
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 39 operand: 30
21	Operation	operator: 25 operands: 26
22	Operation	operator: 28 operands: 27
23	Operation	operator: 28 operands: 29
24	ExprTuple	30
25	Literal
26	ExprTuple	31, 32
27	ExprTuple	41, 33
28	Literal
29	ExprTuple	42, 34
30	Operation	operator: 35 operands: 36
31	Operation	operator: 37 operand: 41
32	Operation	operator: 39 operand: 42
33	Variable
34	Variable
35	Literal
36	ExprTuple	41, 42
37	Literal
38	ExprTuple	41
39	Literal
40	ExprTuple	42
41	Variable
42	Variable