Expression of type And

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, v, w
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Bases, InnerProd
from proveit.logic import And, Equals, Forall, InSet, Set
from proveit.numbers import KroneckerDelta

# build up the expression from sub-expressions
sub_expr1 = Set(x_1_to_n)
expr = And(InSet(sub_expr1, Bases(H)), Forall(instance_param_or_params = [v, w], instance_expr = Equals(InnerProd(v, w), KroneckerDelta(v, w)), domain = sub_expr1))

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(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{Bases}\left(H\right)\right) \land \left[\forall_{v, w \in \left\{x_{1}, x_{2}, \ldots, x_{n}\right\}}~\left(\left \langle v, w\right \rangle = \delta_{v, w}\right)\right]

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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