Expression of type Forall

from the theory of proveit.numbers.integration

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 S
from proveit.core_expr_types import P__x_1_to_n, x_1_to_n
from proveit.logic import Forall, InSet
from proveit.numbers import Real

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = InSet(P__x_1_to_n, Real), domain = S)

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_{x_{1}, x_{2}, \ldots, x_{n} \in S}~\left(P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \in \mathbb{R}\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: 14 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 21 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprRange	lambda_map: 15 start_index: 19 end_index: 20
13	Variable
14	ExprTuple	16
15	Lambda	parameter: 27 body: 17
16	ExprRange	lambda_map: 18 start_index: 19 end_index: 20
17	Operation	operator: 21 operands: 22
18	Lambda	parameter: 27 body: 23
19	Literal
20	Variable
21	Literal
22	ExprTuple	23, 24
23	IndexedVar	variable: 25 index: 27
24	Variable
25	Variable
26	ExprTuple	27
27	Variable