Expression of type And

from the theory of proveit.linear_algebra.tensors

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 ExprRange, IndexedVar, V, Variable, a, i
from proveit.linear_algebra import Norm
from proveit.logic import And, Equals, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
expr = And(ExprRange(sub_expr1, InSet(sub_expr2, IndexedVar(V, sub_expr1)), one, i), And(ExprRange(sub_expr1, Equals(Norm(sub_expr2), one), one, i)))

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(a_{1} \in V_{1}\right) \land  \left(a_{2} \in V_{2}\right) \land  \ldots \land  \left(a_{i} \in V_{i}\right) \land \left(\left(\left \|a_{1}\right \| = 1\right) \land  \left(\left \|a_{2}\right \| = 1\right) \land  \ldots \land  \left(\left \|a_{i}\right \| = 1\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: 5 operands: 1
1	ExprTuple	2, 3
2	ExprRange	lambda_map: 4 start_index: 19 end_index: 12
3	Operation	operator: 5 operands: 6
4	Lambda	parameter: 25 body: 7
5	Literal
6	ExprTuple	8
7	Operation	operator: 9 operands: 10
8	ExprRange	lambda_map: 11 start_index: 19 end_index: 12
9	Literal
10	ExprTuple	22, 13
11	Lambda	parameter: 25 body: 14
12	Variable
13	IndexedVar	variable: 15 index: 25
14	Operation	operator: 16 operands: 17
15	Variable
16	Literal
17	ExprTuple	18, 19
18	Operation	operator: 20 operand: 22
19	Literal
20	Literal
21	ExprTuple	22
22	IndexedVar	variable: 23 index: 25
23	Variable
24	ExprTuple	25
25	Variable