Expression of type Conditional

from the theory of proveit.logic.booleans.conjunction

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, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, 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_l, B_1_to_m, C_1_to_n], instance_expr = Equals(And(A_1_to_l, B_1_to_m, C_1_to_n), And(A_1_to_l, And(B_1_to_m), C_1_to_n)).with_wrapping_at(2), domain = Boolean), And(InSet(l, Natural), InSet(m, Natural), InSet(n, 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_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n} \in \mathbb{B}}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l}\land B_{1} \land  B_{2} \land  \ldots \land  B_{m}\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\right) =  \\ \left(A_{1} \land  A_{2} \land  \ldots \land  A_{l} \land \left(B_{1} \land  B_{2} \land  \ldots \land  B_{m}\right)\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\right) \end{array} \end{array}\right) \textrm{ if } l \in \mathbb{N} ,  m \in \mathbb{N} ,  n \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: 38 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8, 9
6	Lambda	parameters: 25 body: 10
7	Operation	operator: 44 operands: 11
8	Operation	operator: 44 operands: 12
9	Operation	operator: 44 operands: 13
10	Conditional	value: 14 condition: 15
11	ExprTuple	37, 16
12	ExprTuple	52, 16
13	ExprTuple	41, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 38 operands: 19
16	Literal
17	Literal
18	ExprTuple	20, 21
19	ExprTuple	22, 23, 24
20	Operation	operator: 38 operands: 25
21	Operation	operator: 38 operands: 26
22	ExprRange	lambda_map: 27 start_index: 51 end_index: 37
23	ExprRange	lambda_map: 28 start_index: 51 end_index: 52
24	ExprRange	lambda_map: 29 start_index: 51 end_index: 41
25	ExprTuple	30, 46, 32
26	ExprTuple	30, 31, 32
27	Lambda	parameter: 58 body: 33
28	Lambda	parameter: 58 body: 34
29	Lambda	parameter: 58 body: 35
30	ExprRange	lambda_map: 36 start_index: 51 end_index: 37
31	Operation	operator: 38 operands: 39
32	ExprRange	lambda_map: 40 start_index: 51 end_index: 41
33	Operation	operator: 44 operands: 42
34	Operation	operator: 44 operands: 43
35	Operation	operator: 44 operands: 45
36	Lambda	parameter: 58 body: 47
37	Variable
38	Literal
39	ExprTuple	46
40	Lambda	parameter: 58 body: 48
41	Variable
42	ExprTuple	47, 49
43	ExprTuple	55, 49
44	Literal
45	ExprTuple	48, 49
46	ExprRange	lambda_map: 50 start_index: 51 end_index: 52
47	IndexedVar	variable: 53 index: 58
48	IndexedVar	variable: 54 index: 58
49	Literal
50	Lambda	parameter: 58 body: 55
51	Literal
52	Variable
53	Variable
54	Variable
55	IndexedVar	variable: 56 index: 58
56	Variable
57	ExprTuple	58
58	Variable