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 f, i, j
from proveit.core_expr_types import Len, f_i_to_j, iter_ext_equiv
from proveit.logic import Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f, i, j], instance_expr = iter_ext_equiv, 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_{f, i, j~|~|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right)| \in \mathbb{N}}~\left(\begin{array}{c} \begin{array}{l} \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j + 1\right)\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right), f\left(j + 1\right)\right) \end{array} \end{array}\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	30, 24, 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	ExprTuple	16
13	ExprTuple	21, 17
14	Operation	operator: 18 operands: 19
15	Literal
16	ExprRange	lambda_map: 23 start_index: 24 end_index: 22
17	Operation	operator: 30 operand: 22
18	Literal
19	ExprTuple	21
20	ExprTuple	22
21	ExprRange	lambda_map: 23 start_index: 24 end_index: 28
22	Operation	operator: 25 operands: 26
23	Lambda	parameter: 32 body: 27
24	Variable
25	Literal
26	ExprTuple	28, 29
27	Operation	operator: 30 operand: 32
28	Variable
29	Literal
30	Variable
31	ExprTuple	32
32	Variable