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 ExprTuple, 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 = ExprTuple(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())

\left(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]\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: 20 body: 2
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 27 body: 6
5	ExprTuple	27
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 13
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	27, 14
13	Lambda	parameter: 38 body: 15
14	Operation	operator: 16 operand: 20
15	Conditional	value: 18 condition: 19
16	Literal
17	ExprTuple	20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	Variable
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	38, 27
25	Operation	operator: 28 operand: 38
26	Operation	operator: 30 operands: 31
27	Variable
28	Literal
29	ExprTuple	38
30	Literal
31	ExprTuple	32, 33
32	Operation	operator: 34 operands: 35
33	Operation	operator: 36 operands: 37
34	Literal
35	ExprTuple	38, 38
36	Literal
37	ExprTuple	39, 40
38	Variable
39	Literal
40	Literal