Expression of type Forall

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.core_expr_types import P__x_1_to_m_y_1_to_n, R__x_1_to_m_y_1_to_n, y_1_to_n
from proveit.logic import Forall

# build up the expression from sub-expressions
expr = 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)

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())

\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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	12
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 10
7	Operation	operator: 9 operands: 10
8	Variable
9	Variable
10	ExprTuple	11, 12
11	ExprRange	lambda_map: 13 start_index: 16 end_index: 14
12	ExprRange	lambda_map: 15 start_index: 16 end_index: 17
13	Lambda	parameter: 23 body: 18
14	Variable
15	Lambda	parameter: 23 body: 19
16	Literal
17	Variable
18	IndexedVar	variable: 20 index: 23
19	IndexedVar	variable: 21 index: 23
20	Variable
21	Variable
22	ExprTuple	23
23	Variable