Expression of type Forall

from the theory of proveit.numbers.summation

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 Conditional, k
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Interval, eight, nine, one, subtract, two

# build up the expression from sub-expressions
sub_expr1 = subtract(k, two)
expr = Forall(instance_param_or_params = [k], instance_expr = Equals(Conditional(sub_expr1, InSet(k, Interval(Add(eight, one), nine))), Conditional(sub_expr1, InSet(k, Interval(nine, nine)))))

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}~\left(\left\{k - 2 \textrm{ if } k \in \{8 + 1~\ldotp \ldotp~9\}\right.. = \left\{k - 2 \textrm{ if } k \in \{9~\ldotp \ldotp~9\}\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 19 body: 5
4	ExprTuple	19
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Conditional	value: 11 condition: 10
9	Conditional	value: 11 condition: 12
10	Operation	operator: 15 operands: 13
11	Operation	operator: 29 operands: 14
12	Operation	operator: 15 operands: 16
13	ExprTuple	19, 17
14	ExprTuple	19, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 24 operands: 21
18	Operation	operator: 22 operand: 27
19	Variable
20	Operation	operator: 24 operands: 25
21	ExprTuple	26, 28
22	Literal
23	ExprTuple	27
24	Literal
25	ExprTuple	28, 28
26	Operation	operator: 29 operands: 30
27	Literal
28	Literal
29	Literal
30	ExprTuple	31, 32
31	Literal
32	Literal