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, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
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))

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 + 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)

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	6
5	Conditional	value: 7 condition: 8
6	ExprRange	lambda_map: 9 start_index: 34 end_index: 19
7	Operation	operator: 22 operands: 10
8	Operation	operator: 11 operands: 12
9	Lambda	parameter: 33 body: 25
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	15
13	IndexedVar	variable: 28 index: 34
14	IndexedVar	variable: 28 index: 19
15	ExprRange	lambda_map: 18 start_index: 34 end_index: 24
16	ExprTuple	34
17	ExprTuple	19
18	Lambda	parameter: 33 body: 20
19	Operation	operator: 31 operands: 21
20	Operation	operator: 22 operands: 23
21	ExprTuple	24, 34
22	Literal
23	ExprTuple	25, 26
24	Variable
25	IndexedVar	variable: 28 index: 33
26	IndexedVar	variable: 28 index: 30
27	ExprTuple	33
28	Variable
29	ExprTuple	30
30	Operation	operator: 31 operands: 32
31	Literal
32	ExprTuple	33, 34
33	Variable
34	Literal