Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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())

\left(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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 35 body: 3
2	ExprTuple	35
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	35, 11
10	Lambda	parameters: 37 body: 12
11	Operation	operator: 13 operand: 34
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	34
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24
21	Operation	operator: 40 operand: 31
22	Operation	operator: 26 operands: 27
23	Operation	operator: 29 operands: 28
24	Operation	operator: 29 operands: 30
25	ExprTuple	31
26	Literal
27	ExprTuple	32, 33
28	ExprTuple	42, 34
29	Literal
30	ExprTuple	43, 35
31	Operation	operator: 36 operands: 37
32	Operation	operator: 38 operand: 42
33	Operation	operator: 40 operand: 43
34	Variable
35	Variable
36	Literal
37	ExprTuple	42, 43
38	Literal
39	ExprTuple	42
40	Literal
41	ExprTuple	43
42	Variable
43	Variable