Expression of type Lambda

from the theory of proveit.logic.booleans.quantification

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 Conditional, Lambda
from proveit.core_expr_types import P__x_1_to_m_y_1_to_n, Q__x_1_to_m, R__x_1_to_m_y_1_to_n, x_1_to_m, y_1_to_n
from proveit.logic import Forall

# build up the expression from sub-expressions
expr = Lambda([x_1_to_m], Conditional(Forall(instance_param_or_params = [y_1_to_n], instance_expr = P__x_1_to_m_y_1_to_n, condition = R__x_1_to_m_y_1_to_n), Q__x_1_to_m))

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(x_{1}, x_{2}, \ldots, x_{m}\right) \mapsto \left\{\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~R\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{m},y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } Q\left(x_{1}, x_{2}, \ldots, x_{m}\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: 7 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 8
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8
6	Variable
7	ExprTuple	16
8	Lambda	parameters: 9 body: 10
9	ExprTuple	17
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, 17
16	ExprRange	lambda_map: 18 start_index: 21 end_index: 19
17	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
18	Lambda	parameter: 28 body: 23
19	Variable
20	Lambda	parameter: 28 body: 24
21	Literal
22	Variable
23	IndexedVar	variable: 25 index: 28
24	IndexedVar	variable: 26 index: 28
25	Variable
26	Variable
27	ExprTuple	28
28	Variable