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
expr = Conditional(Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C_1_to_n], instance_expr = And(A_1_to_l, And(B_1_to_m), C_1_to_n), condition = And(A_1_to_l, B_1_to_m, C_1_to_n)), 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(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) \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: 23 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8, 9
6	Lambda	parameters: 19 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	26, 17
12	ExprTuple	34, 17
13	Literal
14	ExprTuple	28, 17
15	Operation	operator: 23 operands: 18
16	Operation	operator: 23 operands: 19
17	Literal
18	ExprTuple	21, 20, 22
19	ExprTuple	21, 29, 22
20	Operation	operator: 23 operands: 24
21	ExprRange	lambda_map: 25 start_index: 33 end_index: 26
22	ExprRange	lambda_map: 27 start_index: 33 end_index: 28
23	Literal
24	ExprTuple	29
25	Lambda	parameter: 40 body: 30
26	Variable
27	Lambda	parameter: 40 body: 31
28	Variable
29	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
30	IndexedVar	variable: 35 index: 40
31	IndexedVar	variable: 36 index: 40
32	Lambda	parameter: 40 body: 37
33	Literal
34	Variable
35	Variable
36	Variable
37	IndexedVar	variable: 38 index: 40
38	Variable
39	ExprTuple	40
40	Variable