Expression of type And

from the theory of proveit.numbers.multiplication

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, Variable, a, n
from proveit.logic import And, Equals, InSet, Or
from proveit.numbers import Complex, one, zero

# 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, Complex), one, n), Or(ExprRange(sub_expr1, Equals(sub_expr2, zero), one, n)))

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 \mathbb{C}\right) \land  \left(a_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(a_{n} \in \mathbb{C}\right) \land \left(\left(a_{1} = 0\right) \lor  \left(a_{2} = 0\right) \lor  \ldots \lor  \left(a_{n} = 0\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: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	ExprRange	lambda_map: 5 start_index: 13 end_index: 14
4	Operation	operator: 6 operands: 7
5	Lambda	parameter: 23 body: 8
6	Literal
7	ExprTuple	9
8	Operation	operator: 10 operands: 11
9	ExprRange	lambda_map: 12 start_index: 13 end_index: 14
10	Literal
11	ExprTuple	19, 15
12	Lambda	parameter: 23 body: 16
13	Literal
14	Variable
15	Literal
16	Operation	operator: 17 operands: 18
17	Literal
18	ExprTuple	19, 20
19	IndexedVar	variable: 21 index: 23
20	Literal
21	Variable
22	ExprTuple	23
23	Variable