Expression of type And

from the theory of proveit.core_expr_types.tuples

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 a, b, i, j, k, l
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Natural, one, subtract

# build up the expression from sub-expressions
expr = And(InSet(subtract(Add(j, one), i), Natural), Equals(Add(i, a), Add(k, b)), Equals(Add(j, a), Add(l, b)))

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(\left(j + 1\right) - i\right) \in \mathbb{N}\right) \land \left(\left(i + a\right) = \left(k + b\right)\right) \land \left(\left(j + a\right) = \left(l + b\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, 5
3	Operation	operator: 6 operands: 7
4	Operation	operator: 9 operands: 8
5	Operation	operator: 9 operands: 10
6	Literal
7	ExprTuple	11, 12
8	ExprTuple	13, 14
9	Literal
10	ExprTuple	15, 16
11	Operation	operator: 28 operands: 17
12	Literal
13	Operation	operator: 28 operands: 18
14	Operation	operator: 28 operands: 19
15	Operation	operator: 28 operands: 20
16	Operation	operator: 28 operands: 21
17	ExprTuple	22, 23
18	ExprTuple	34, 25
19	ExprTuple	24, 27
20	ExprTuple	32, 25
21	ExprTuple	26, 27
22	Operation	operator: 28 operands: 29
23	Operation	operator: 30 operand: 34
24	Variable
25	Variable
26	Variable
27	Variable
28	Literal
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	34
32	Variable
33	Literal
34	Variable