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.logic import And, Equals, InSet
from proveit.numbers import Digits, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(c, sub_expr1)
expr = And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Digits), one, m), InSet(b, Digits), ExprRange(sub_expr1, InSet(sub_expr2, Digits), one, n), ExprRange(sub_expr1, InSet(IndexedVar(d, sub_expr1), Digits), one, k), Equals([ExprRange(sub_expr1, b, one, n)], [ExprRange(sub_expr1, sub_expr2, 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{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 \in \mathbb{N}^{\leq 9}\right)\land \left(c_{1} \in \mathbb{N}^{\leq 9}\right) \land  \left(c_{2} \in \mathbb{N}^{\leq 9}\right) \land  \ldots \land  \left(c_{n} \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, b, ..\left(n - 3\right) \times.., b\right) = \left(c_{1}, c_{2}, \ldots, c_{n}\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, 6, 7
3	ExprRange	lambda_map: 8 start_index: 32 end_index: 9
4	Operation	operator: 23 operands: 10
5	ExprRange	lambda_map: 11 start_index: 32 end_index: 33
6	ExprRange	lambda_map: 12 start_index: 32 end_index: 13
7	Operation	operator: 14 operands: 15
8	Lambda	parameter: 40 body: 16
9	Variable
10	ExprTuple	36, 29
11	Lambda	parameter: 40 body: 17
12	Lambda	parameter: 40 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	ExprTuple	25
20	ExprTuple	26
21	ExprTuple	27, 29
22	ExprTuple	37, 29
23	Literal
24	ExprTuple	28, 29
25	ExprRange	lambda_map: 30 start_index: 32 end_index: 33
26	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
27	IndexedVar	variable: 34 index: 40
28	IndexedVar	variable: 35 index: 40
29	Literal
30	Lambda	parameter: 40 body: 36
31	Lambda	parameter: 40 body: 37
32	Literal
33	Variable
34	Variable
35	Variable
36	Variable
37	IndexedVar	variable: 38 index: 40
38	Variable
39	ExprTuple	40
40	Variable