Expression of type Forall

from the theory of proveit.linear_algebra.vector_sets

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 V, n
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Bases, Dim
from proveit.logic import Equals, Forall, InSet, Set
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(Dim(V), n), condition = InSet(Set(x_1_to_n), Bases(V))), domain = NaturalPos)

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_{n \in \mathbb{N}^+}~\left[\forall_{x_{1}, x_{2}, \ldots, x_{n}~|~\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{Bases}\left(V\right)}~\left(\textrm{Dim}\left(V\right) = n\right)\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 31 body: 4
3	ExprTuple	31
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 17 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	31, 11
10	Lambda	parameters: 24 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 31
17	Literal
18	ExprTuple	20, 21
19	Operation	operator: 22 operand: 28
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operand: 28
22	Literal
23	Literal
24	ExprTuple	27
25	Literal
26	ExprTuple	28
27	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
28	Variable
29	Lambda	parameter: 35 body: 32
30	Literal
31	Variable
32	IndexedVar	variable: 33 index: 35
33	Variable
34	ExprTuple	35
35	Variable