Expression of type ExprTuple

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, ExprTuple, Lambda, 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 = ExprTuple(Lambda(m, 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(m \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 39 body: 3
2	ExprTuple	39
3	Conditional	value: 4 condition: 5
4	Operation	operator: 20 operand: 8
5	Operation	operator: 29 operands: 7
6	ExprTuple	8
7	ExprTuple	39, 9
8	Lambda	parameters: 15 body: 10
9	Literal
10	Operation	operator: 11 operands: 12
11	Literal
12	ExprTuple	13, 14
13	Operation	operator: 27 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	36, 31
16	Literal
17	ExprTuple	18, 19
18	Operation	operator: 27 operands: 35
19	Operation	operator: 20 operand: 22
20	Literal
21	ExprTuple	22
22	Lambda	parameter: 32 body: 24
23	ExprTuple	32
24	Conditional	value: 25 condition: 26
25	Operation	operator: 27 operands: 28
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	32, 31
29	Literal
30	ExprTuple	32, 33
31	Variable
32	Variable
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36
36	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
37	Lambda	parameter: 43 body: 40
38	Literal
39	Variable
40	IndexedVar	variable: 41 index: 43
41	Variable
42	ExprTuple	43
43	Variable