Expression of type Lambda

from the theory of proveit.logic.sets.equivalence

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, a, b, c, x
from proveit.logic import Equals, InSet, Set
from proveit.numbers import one, three, two

# build up the expression from sub-expressions
expr = Lambda(x, Equals(InSet(x, Set(one, two, three)), InSet(x, Set(a, b, c))))

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())

x \mapsto \left(\left(x \in \left\{1, 2, 3\right\}\right) = \left(x \in \left\{a, b, c\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	parameter: 11 body: 2
1	ExprTuple	11
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 8 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	11, 10
8	Literal
9	ExprTuple	11, 12
10	Operation	operator: 14 operands: 13
11	Variable
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 17, 18
14	Literal
15	ExprTuple	19, 20, 21
16	Literal
17	Literal
18	Literal
19	Variable
20	Variable
21	Variable