Expression of type Lambda

from the theory of proveit.logic.booleans.quantification.universality

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, P, Q
from proveit.logic import Boolean, InSet
from proveit.logic.booleans.quantification import general_forall_Px_if_Qx

# build up the expression from sub-expressions
expr = Lambda([P, Q], InSet(general_forall_Px_if_Qx, Boolean))

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(P, Q\right) \mapsto \left(\left[\forall_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right] \in \mathbb{B}\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	13, 14
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 7 operand: 9
6	Literal
7	Literal
8	ExprTuple	9
9	Lambda	parameters: 15 body: 10
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 15
12	Operation	operator: 14 operands: 15
13	Variable
14	Variable
15	ExprTuple	16
16	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
17	Lambda	parameter: 23 body: 20
18	Literal
19	Variable
20	IndexedVar	variable: 21 index: 23
21	Variable
22	ExprTuple	23
23	Variable