Expression of type And

from the theory of proveit.numbers.numerals.decimals

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, d, k, m, n
from proveit.core_expr_types import b_1_to_n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Digits, 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), Digits), one, m), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Digits), one, n), InSet(c, Digits), ExprRange(sub_expr1, InSet(IndexedVar(d, sub_expr1), Digits), one, k), Equals(Add(b_1_to_n), c))

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{N}^{\leq 9}\right) \land  \left(a_{2} \in \mathbb{N}^{\leq 9}\right) \land  \ldots \land  \left(a_{m} \in \mathbb{N}^{\leq 9}\right)\land \left(b_{1} \in \mathbb{N}^{\leq 9}\right) \land  \left(b_{2} \in \mathbb{N}^{\leq 9}\right) \land  \ldots \land  \left(b_{n} \in \mathbb{N}^{\leq 9}\right) \land \left(c \in \mathbb{N}^{\leq 9}\right)\land \left(d_{1} \in \mathbb{N}^{\leq 9}\right) \land  \left(d_{2} \in \mathbb{N}^{\leq 9}\right) \land  \ldots \land  \left(d_{k} \in \mathbb{N}^{\leq 9}\right) \land \left(\left(b_{1} +  b_{2} +  \ldots +  b_{n}\right) = c\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, 7
3	ExprRange	lambda_map: 8 start_index: 34 end_index: 9
4	ExprRange	lambda_map: 10 start_index: 34 end_index: 35
5	Operation	operator: 23 operands: 11
6	ExprRange	lambda_map: 12 start_index: 34 end_index: 13
7	Operation	operator: 14 operands: 15
8	Lambda	parameter: 39 body: 16
9	Variable
10	Lambda	parameter: 39 body: 17
11	ExprTuple	20, 29
12	Lambda	parameter: 39 body: 18
13	Variable
14	Literal
15	ExprTuple	19, 20
16	Operation	operator: 23 operands: 21
17	Operation	operator: 23 operands: 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 25 operands: 26
20	Variable
21	ExprTuple	27, 29
22	ExprTuple	36, 29
23	Literal
24	ExprTuple	28, 29
25	Literal
26	ExprTuple	30
27	IndexedVar	variable: 31 index: 39
28	IndexedVar	variable: 32 index: 39
29	Literal
30	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
31	Variable
32	Variable
33	Lambda	parameter: 39 body: 36
34	Literal
35	Variable
36	IndexedVar	variable: 37 index: 39
37	Variable
38	ExprTuple	39
39	Variable