Expression of type ExprTuple

from the theory of proveit.logic.sets.comprehension

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, Q, Qx, S, x
from proveit.logic import Forall, InSet
from proveit.logic.sets import basic_comprehension_y

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([S, Q], Forall(instance_param_or_params = [x], instance_expr = InSet(x, basic_comprehension_y), domain = S, condition = Qx)))

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, Q\right) \mapsto \left[\forall_{x \in S~|~Q\left(x\right)}~\left(x \in \left\{y~|~Q\left(y\right)\right\}_{y \in S}\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	31, 29
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameter: 20 body: 7
7	Conditional	value: 8 condition: 9
8	Operation	operator: 27 operands: 10
9	Operation	operator: 23 operands: 11
10	ExprTuple	20, 12
11	ExprTuple	13, 14
12	Operation	operator: 15 operand: 19
13	Operation	operator: 27 operands: 17
14	Operation	operator: 29 operand: 20
15	Literal
16	ExprTuple	19
17	ExprTuple	20, 31
18	ExprTuple	20
19	Lambda	parameter: 32 body: 21
20	Variable
21	Conditional	value: 32 condition: 22
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26
25	Operation	operator: 27 operands: 28
26	Operation	operator: 29 operand: 32
27	Literal
28	ExprTuple	32, 31
29	Variable
30	ExprTuple	32
31	Variable
32	Variable