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, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
sub_expr1 = [A_1_to_l, B_1_to_m, C_1_to_n]
expr = Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = And(B_1_to_m), conditions = sub_expr1), 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}~|~A_{1}, A_{2}, \ldots, A_{l},B_{1}, B_{2}, \ldots, B_{m},C_{1}, C_{2}, \ldots, C_{n}}~\left(B_{1} \land  B_{2} \land  \ldots \land  B_{m}\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: 19 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8, 9
6	Lambda	parameters: 20 body: 10
7	Operation	operator: 13 operands: 11
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	Conditional	value: 15 condition: 16
11	ExprTuple	25, 17
12	ExprTuple	27, 17
13	Literal
14	ExprTuple	30, 17
15	Operation	operator: 19 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	22
19	Literal
20	ExprTuple	21, 22, 23
21	ExprRange	lambda_map: 24 start_index: 29 end_index: 25
22	ExprRange	lambda_map: 26 start_index: 29 end_index: 27
23	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
24	Lambda	parameter: 38 body: 31
25	Variable
26	Lambda	parameter: 38 body: 32
27	Variable
28	Lambda	parameter: 38 body: 33
29	Literal
30	Variable
31	IndexedVar	variable: 34 index: 38
32	IndexedVar	variable: 35 index: 38
33	IndexedVar	variable: 36 index: 38
34	Variable
35	Variable
36	Variable
37	ExprTuple	38
38	Variable