Expression of type Lambda

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 Lambda
from proveit.core_expr_types import x_1_to_n
from proveit.logic import Disjoint, Distinct, Equals
from proveit.logic.sets import x_singletons_range

# build up the expression from sub-expressions
expr = Lambda([x_1_to_n], Equals(Distinct(x_1_to_n), Disjoint(x_singletons_range)))

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(x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \left(\textrm{distinct}\left(x_{1}, x_{2}, \ldots, x_{n}\right) = \textrm{disjoint}\left(\left\{x_{1}\right\}, \left\{x_{2}\right\}, \ldots, \left\{x_{n}\right\}\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 7 body: 1
1	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11
10	ExprRange	lambda_map: 12 start_index: 14 end_index: 15
11	ExprRange	lambda_map: 13 start_index: 14 end_index: 15
12	Lambda	parameter: 22 body: 19
13	Lambda	parameter: 22 body: 16
14	Literal
15	Variable
16	Operation	operator: 17 operand: 19
17	Literal
18	ExprTuple	19
19	IndexedVar	variable: 20 index: 22
20	Variable
21	ExprTuple	22
22	Variable