Expression of type Forall

from the theory of proveit.core_expr_types.tuples

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 i, j, x
from proveit.core_expr_types import Len, f_i_to_j
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Natural, Neg, two

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [i, j], instance_expr = Equals(Len(operands = [f_i_to_j, x]), Add(j, Neg(i), two)), condition = InSet(Len(operands = [f_i_to_j]), Natural))

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_{i, j~|~|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right)| \in \mathbb{N}}~\left(|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right), x\right)| = \left(j - i + 2\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	parameters: 4 body: 5
4	ExprTuple	29, 28
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	14, 15
12	Operation	operator: 19 operands: 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 19 operands: 20
15	Literal
16	ExprTuple	24, 21
17	Literal
18	ExprTuple	28, 22, 23
19	Literal
20	ExprTuple	24
21	Variable
22	Operation	operator: 25 operand: 29
23	Literal
24	ExprRange	lambda_map: 27 start_index: 29 end_index: 28
25	Literal
26	ExprTuple	29
27	Lambda	parameter: 33 body: 30
28	Variable
29	Variable
30	Operation	operator: 31 operand: 33
31	Variable
32	ExprTuple	33
33	Variable