Expression of type Forall

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

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 alpha
from proveit.core_expr_types import P__x_1_to_n, Q__x_1_to_n, x_1_to_n
from proveit.logic import Forall, Implies

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = Implies(P__x_1_to_n, alpha), condition = Q__x_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_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~\left(P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \Rightarrow \alpha\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: 13 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 13
7	Literal
8	ExprTuple	10, 11
9	Variable
10	Operation	operator: 12 operands: 13
11	Variable
12	Variable
13	ExprTuple	14
14	ExprRange	lambda_map: 15 start_index: 16 end_index: 17
15	Lambda	parameter: 21 body: 18
16	Literal
17	Variable
18	IndexedVar	variable: 19 index: 21
19	Variable
20	ExprTuple	21
21	Variable