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, b, i, j, x, y
from proveit.logic import And, InSet
from proveit.numbers import Less, RealPos, one

# 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), RealPos), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), RealPos), one, j), Less(x, y))

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