Expression of type Conditional

from the theory of proveit.logic.sets.disjointness

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 B, Conditional, X, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import And, Disjoint, Forall, Iff, InSet, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A_1_to_m, B], instance_expr = Iff(Disjoint(A_1_to_m, B), And(Disjoint(A_1_to_m), Forall(instance_param_or_params = [X], instance_expr = Disjoint(X, B), domain = Set(A_1_to_m)))).with_wrapping_at(2)), InSet(m, 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}~\left(\begin{array}{c} \begin{array}{l} \textrm{disjoint}\left(A_{1}, A_{2}, \ldots, A_{m}, B\right) \Leftrightarrow  \\ \left(\textrm{disjoint}\left(A_{1}, A_{2}, \ldots, A_{m}\right) \land \left[\forall_{X \in \left\{A_{1}, A_{2}, \ldots, A_{m}\right\}}~\textrm{disjoint}\left(X, B\right)\right]\right) \end{array} \end{array}\right) \textrm{ if } m \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: 17 operand: 5
2	Operation	operator: 26 operands: 4
3	ExprTuple	5
4	ExprTuple	36, 6
5	Lambda	parameters: 12 body: 7
6	Literal
7	Operation	operator: 8 operands: 9
8	Literal
9	ExprTuple	10, 11
10	Operation	operator: 24 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	33, 28
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 24 operands: 32
16	Operation	operator: 17 operand: 19
17	Literal
18	ExprTuple	19
19	Lambda	parameter: 29 body: 21
20	ExprTuple	29
21	Conditional	value: 22 condition: 23
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	29, 28
26	Literal
27	ExprTuple	29, 30
28	Variable
29	Variable
30	Operation	operator: 31 operands: 32
31	Literal
32	ExprTuple	33
33	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
34	Lambda	parameter: 40 body: 37
35	Literal
36	Variable
37	IndexedVar	variable: 38 index: 40
38	Variable
39	ExprTuple	40
40	Variable