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, m
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Interval, one, subtract

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

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