Expression of type Forall

from the theory of proveit.logic.equality

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 ExprRange, IndexedVar, Variable, n, x
from proveit.core_expr_types import x_1_to_np1
from proveit.logic import Equals, Forall
from proveit.numbers import Add, NaturalPos, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [x_1_to_np1], instance_expr = Equals(IndexedVar(x, one), IndexedVar(x, Add(n, one))), condition = ExprRange(sub_expr1, Equals(IndexedVar(x, sub_expr1), IndexedVar(x, Add(sub_expr1, one))), one, n)), 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 + 1}~|~\left(x_{1} = x_{1 + 1}\right), \left(x_{2} = x_{2 + 1}\right), \ldots, \left(x_{n} = x_{n + 1}\right)}~\left(x_{1} = x_{n + 1}\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: 33 body: 4
3	ExprTuple	33
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	33, 12
11	Lambda	parameters: 13 body: 14
12	Literal
13	ExprTuple	15
14	Conditional	value: 16 condition: 17
15	ExprRange	lambda_map: 18 start_index: 43 end_index: 28
16	Operation	operator: 31 operands: 19
17	Operation	operator: 20 operands: 21
18	Lambda	parameter: 42 body: 34
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24
22	IndexedVar	variable: 37 index: 43
23	IndexedVar	variable: 37 index: 28
24	ExprRange	lambda_map: 27 start_index: 43 end_index: 33
25	ExprTuple	43
26	ExprTuple	28
27	Lambda	parameter: 42 body: 29
28	Operation	operator: 40 operands: 30
29	Operation	operator: 31 operands: 32
30	ExprTuple	33, 43
31	Literal
32	ExprTuple	34, 35
33	Variable
34	IndexedVar	variable: 37 index: 42
35	IndexedVar	variable: 37 index: 39
36	ExprTuple	42
37	Variable
38	ExprTuple	39
39	Operation	operator: 40 operands: 41
40	Literal
41	ExprTuple	42, 43
42	Variable
43	Literal