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

# build up the expression from sub-expressions
expr = Lambda([S, y], Forall(instance_param_or_params = [x], instance_expr = And(InSet(x, S), NotEquals(x, y)), domain = 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())

\left(S, y\right) \mapsto \left[\forall_{x \in S - \left\{y\right\}}~\left(\left(x \in S\right) \land \left(x \neq 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	parameters: 1 body: 2
1	ExprTuple	23, 27
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameter: 22 body: 7
6	ExprTuple	22
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 16 operands: 12
10	Literal
11	ExprTuple	13, 14
12	ExprTuple	22, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operands: 21
16	Literal
17	ExprTuple	22, 23
18	Literal
19	ExprTuple	22, 27
20	Literal
21	ExprTuple	23, 24
22	Variable
23	Variable
24	Operation	operator: 25 operand: 27
25	Literal
26	ExprTuple	27
27	Variable