Expression of type Lambda

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 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 = 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(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]

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	30, 28
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameter: 19 body: 6
6	Conditional	value: 7 condition: 8
7	Operation	operator: 26 operands: 9
8	Operation	operator: 22 operands: 10
9	ExprTuple	19, 11
10	ExprTuple	12, 13
11	Operation	operator: 14 operand: 18
12	Operation	operator: 26 operands: 16
13	Operation	operator: 28 operand: 19
14	Literal
15	ExprTuple	18
16	ExprTuple	19, 30
17	ExprTuple	19
18	Lambda	parameter: 31 body: 20
19	Variable
20	Conditional	value: 31 condition: 21
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	24, 25
24	Operation	operator: 26 operands: 27
25	Operation	operator: 28 operand: 31
26	Literal
27	ExprTuple	31, 30
28	Variable
29	ExprTuple	31
30	Variable
31	Variable