Expression of type ExprTuple

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 ExprTuple, Lambda, S, x, y
from proveit.logic import Difference, Equals, Forall, NotInSet, Or, Set

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([S, y], Forall(instance_param_or_params = [x], instance_expr = NotInSet(x, Difference(S, Set(y))), condition = Or(NotInSet(x, S), Equals(x, 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(\left(S, y\right) \mapsto \left[\forall_{x~|~\left(x \notin S\right) \lor \left(x = y\right)}~\left(x \notin \left(S - \left\{y\right\}\right)\right)\right]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	24, 28
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameter: 25 body: 8
7	ExprTuple	25
8	Conditional	value: 9 condition: 10
9	Operation	operator: 19 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	25, 14
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operands: 22
17	Literal
18	ExprTuple	24, 23
19	Literal
20	ExprTuple	25, 24
21	Literal
22	ExprTuple	25, 28
23	Operation	operator: 26 operand: 28
24	Variable
25	Variable
26	Literal
27	ExprTuple	28
28	Variable