Expression of type Forall

from the theory of proveit.numbers.numerals.decimals

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, Variable, k
from proveit.logic import Equals, Forall
from proveit.numbers import Add, DecimalSequence, NaturalPos, nine, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [k], instance_expr = Equals(Add(DecimalSequence(ExprRange(sub_expr1, nine, one, k)), one), DecimalSequence(one, ExprRange(sub_expr1, zero, one, k))), 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_{k \in \mathbb{N}^+}~\left(\left(\texttt{\#}(9, 9, ..\left(k - 3\right) \times.., 9) + 1\right) = \texttt{\#}(1 ~ 0, 0, ..\left(k - 3\right) \times.., 0)\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	parameter: 27 body: 5
4	ExprTuple	27
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	27, 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 20 operands: 17
14	Literal
15	Literal
16	ExprTuple	18, 26
17	ExprTuple	26, 19
18	Operation	operator: 20 operands: 21
19	ExprRange	lambda_map: 22 start_index: 26 end_index: 27
20	Literal
21	ExprTuple	23
22	Lambda	parameter: 30 body: 24
23	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
24	Literal
25	Lambda	parameter: 30 body: 29
26	Literal
27	Variable
28	ExprTuple	30
29	Literal
30	Variable