Expression of type And

from the theory of proveit.numbers.addition

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, b, c, i, j
from proveit.logic import And, InSet
from proveit.numbers import Less, RationalNonPos, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), RationalNonPos), one, i), InSet(b, RationalNonPos), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), RationalNonPos), one, j), Less(b, zero))

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{Q}^{\leq 0}\right) \land  \left(a_{2} \in \mathbb{Q}^{\leq 0}\right) \land  \ldots \land  \left(a_{i} \in \mathbb{Q}^{\leq 0}\right) \land \left(b \in \mathbb{Q}^{\leq 0}\right)\land \left(c_{1} \in \mathbb{Q}^{\leq 0}\right) \land  \left(c_{2} \in \mathbb{Q}^{\leq 0}\right) \land  \ldots \land  \left(c_{j} \in \mathbb{Q}^{\leq 0}\right) \land \left(b < 0\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, 5, 6
3	ExprRange	lambda_map: 7 start_index: 11 end_index: 8
4	Operation	operator: 20 operands: 9
5	ExprRange	lambda_map: 10 start_index: 11 end_index: 12
6	Operation	operator: 13 operands: 14
7	Lambda	parameter: 28 body: 15
8	Variable
9	ExprTuple	17, 24
10	Lambda	parameter: 28 body: 16
11	Literal
12	Variable
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 20 operands: 19
16	Operation	operator: 20 operands: 21
17	Variable
18	Literal
19	ExprTuple	22, 24
20	Literal
21	ExprTuple	23, 24
22	IndexedVar	variable: 25 index: 28
23	IndexedVar	variable: 26 index: 28
24	Literal
25	Variable
26	Variable
27	ExprTuple	28
28	Variable