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 A, B, C, Conditional, Lambda
from proveit.logic import And, SetEquiv

# build up the expression from sub-expressions
expr = Lambda([A, B, C], Conditional(SetEquiv(A, C), And(SetEquiv(A, B), SetEquiv(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())

\left(A, B, C\right) \mapsto \left\{A \cong C \textrm{ if } A \cong B ,  B \cong C\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	13, 14, 15
2	Conditional	value: 3 condition: 4
3	Operation	operator: 11 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	13, 15
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 11 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	14, 15
13	Variable
14	Variable
15	Variable