Expression of type Conditional

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 Conditional, ExprRange, IndexedVar, Variable, a, b, c, d, k, m, n
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import DecimalSequence, Digits, Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = ExprRange(sub_expr1, b, one, n)
sub_expr3 = ExprRange(sub_expr1, IndexedVar(a, sub_expr1), one, m)
sub_expr4 = ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, n)
sub_expr5 = ExprRange(sub_expr1, IndexedVar(d, sub_expr1), one, k)
expr = Conditional(Forall(instance_param_or_params = [sub_expr3, b, sub_expr4, sub_expr5], instance_expr = Equals(DecimalSequence(sub_expr3, sub_expr2, sub_expr5), DecimalSequence(sub_expr3, sub_expr4, sub_expr5)), domain = Digits, condition = Equals([sub_expr2], [sub_expr4])), And(InSet(m, Natural), InSet(n, Natural), InSet(k, Natural)))

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\{\forall_{a_{1}, a_{2}, \ldots, a_{m}, b, c_{1}, c_{2}, \ldots, c_{n}, d_{1}, d_{2}, \ldots, d_{k} \in \mathbb{N}^{\leq 9}~|~\left(b, b, ..\left(n - 3\right) \times.., b\right) = \left(c_{1}, c_{2}, \ldots, c_{n}\right)}~\left(\texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ b, b, ..\left(n - 3\right) \times.., b ~ d_{1}, d_{2}, \ldots, d_{k}) = \texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ c_{1}, c_{2}, \ldots, c_{n} ~ d_{1}, d_{2}, \ldots, d_{k})\right) \textrm{ if } m \in \mathbb{N} ,  n \in \mathbb{N} ,  k \in \mathbb{N}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 19 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8, 9
6	Lambda	parameters: 10 body: 11
7	Operation	operator: 50 operands: 12
8	Operation	operator: 50 operands: 13
9	Operation	operator: 50 operands: 14
10	ExprTuple	37, 63, 53, 38
11	Conditional	value: 15 condition: 16
12	ExprTuple	45, 17
13	ExprTuple	60, 17
14	ExprTuple	47, 17
15	Operation	operator: 35 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24, 25, 26, 27
21	Operation	operator: 29 operands: 28
22	Operation	operator: 29 operands: 30
23	ExprRange	lambda_map: 31 start_index: 59 end_index: 45
24	Operation	operator: 50 operands: 32
25	ExprRange	lambda_map: 33 start_index: 59 end_index: 60
26	ExprRange	lambda_map: 34 start_index: 59 end_index: 47
27	Operation	operator: 35 operands: 36
28	ExprTuple	37, 52, 38
29	Literal
30	ExprTuple	37, 53, 38
31	Lambda	parameter: 67 body: 39
32	ExprTuple	63, 56
33	Lambda	parameter: 67 body: 40
34	Lambda	parameter: 67 body: 41
35	Literal
36	ExprTuple	42, 43
37	ExprRange	lambda_map: 44 start_index: 59 end_index: 45
38	ExprRange	lambda_map: 46 start_index: 59 end_index: 47
39	Operation	operator: 50 operands: 48
40	Operation	operator: 50 operands: 49
41	Operation	operator: 50 operands: 51
42	ExprTuple	52
43	ExprTuple	53
44	Lambda	parameter: 67 body: 54
45	Variable
46	Lambda	parameter: 67 body: 55
47	Variable
48	ExprTuple	54, 56
49	ExprTuple	64, 56
50	Literal
51	ExprTuple	55, 56
52	ExprRange	lambda_map: 57 start_index: 59 end_index: 60
53	ExprRange	lambda_map: 58 start_index: 59 end_index: 60
54	IndexedVar	variable: 61 index: 67
55	IndexedVar	variable: 62 index: 67
56	Literal
57	Lambda	parameter: 67 body: 63
58	Lambda	parameter: 67 body: 64
59	Literal
60	Variable
61	Variable
62	Variable
63	Variable
64	IndexedVar	variable: 65 index: 67
65	Variable
66	ExprTuple	67
67	Variable