Expression of type Conditional

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 Conditional, i, j, k
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k, d_1_to_j
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j, c_1_to_k, d_1_to_j], instance_expr = Equals([a_1_to_i, b_1_to_j, c_1_to_k], [a_1_to_i, d_1_to_j, c_1_to_k]).with_wrapping_at(2), condition = Equals([b_1_to_j], [d_1_to_j])), And(InSet(i, Natural), InSet(j, 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_{i}, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k}, d_{1}, d_{2}, \ldots, d_{j}~|~\left(b_{1}, b_{2}, \ldots, b_{j}\right) = \left(d_{1}, d_{2}, \ldots, d_{j}\right)}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1}, a_{2}, \ldots, a_{i},b_{1}, b_{2}, \ldots, b_{j},c_{1}, c_{2}, \ldots, c_{k}\right) =  \\ \left(a_{1}, a_{2}, \ldots, a_{i},d_{1}, d_{2}, \ldots, d_{j},c_{1}, c_{2}, \ldots, c_{k}\right) \end{array} \end{array}\right) \textrm{ if } i \in \mathbb{N} ,  j \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: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9, 10
7	Lambda	parameters: 11 body: 12
8	Operation	operator: 15 operands: 13
9	Operation	operator: 15 operands: 14
10	Operation	operator: 15 operands: 16
11	ExprTuple	27, 29, 28, 30
12	Conditional	value: 17 condition: 18
13	ExprTuple	32, 19
14	ExprTuple	38, 19
15	Literal
16	ExprTuple	34, 19
17	Operation	operator: 21 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26
23	ExprTuple	27, 29, 28
24	ExprTuple	27, 30, 28
25	ExprTuple	29
26	ExprTuple	30
27	ExprRange	lambda_map: 31 start_index: 37 end_index: 32
28	ExprRange	lambda_map: 33 start_index: 37 end_index: 34
29	ExprRange	lambda_map: 35 start_index: 37 end_index: 38
30	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
31	Lambda	parameter: 48 body: 39
32	Variable
33	Lambda	parameter: 48 body: 40
34	Variable
35	Lambda	parameter: 48 body: 41
36	Lambda	parameter: 48 body: 42
37	Literal
38	Variable
39	IndexedVar	variable: 43 index: 48
40	IndexedVar	variable: 44 index: 48
41	IndexedVar	variable: 45 index: 48
42	IndexedVar	variable: 46 index: 48
43	Variable
44	Variable
45	Variable
46	Variable
47	ExprTuple	48
48	Variable