Expression of type Lambda

from the theory of proveit.logic.sets.subtraction

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 Conditional, Lambda, S, x, y
from proveit.logic import And, Difference, InSet, NotEquals, Set

# build up the expression from sub-expressions
expr = Lambda(x, Conditional(And(InSet(x, S), NotEquals(x, y)), InSet(x, Difference(S, Set(y)))))

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 S\right) \land \left(x \neq y\right) \textrm{ if } x \in \left(S - \left\{y\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: 17 body: 2
1	ExprTuple	17
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 11 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	17, 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operands: 16
11	Literal
12	ExprTuple	17, 18
13	Literal
14	ExprTuple	17, 22
15	Literal
16	ExprTuple	18, 19
17	Variable
18	Variable
19	Operation	operator: 20 operand: 22
20	Literal
21	ExprTuple	22
22	Variable