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
from proveit.core_expr_types.tuples import general_range_of_ranges
from proveit.logic import Equals, Forall
from proveit.numbers import zero

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f, i, j], instance_expr = Equals(Len(operands = general_range_of_ranges), zero).with_wrapping_at(1))

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(\begin{array}{c} \begin{array}{l} |\left(f\left(m, i\left(m\right)\right), f\left(m, i\left(m\right) + 1\right), \ldots, f\left(m, j\left(m\right)\right), f\left(m + 1, i\left(m + 1\right)\right), f\left(m + 1, i\left(m + 1\right) + 1\right), \ldots, f\left(m + 1, j\left(m + 1\right)\right), \ldots\ldots, f\left(n, i\left(n\right)\right), f\left(n, i\left(n\right) + 1\right), \ldots, f\left(n, j\left(n\right)\right)\right)| \\  = 0 \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	25, 22, 23
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 10 operands: 11
9	Literal
10	Literal
11	ExprTuple	12
12	ExprRange	lambda_map: 13 start_index: 14 end_index: 15
13	Lambda	parameter: 27 body: 16
14	Variable
15	Variable
16	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
17	Lambda	parameter: 28 body: 21
18	Operation	operator: 22 operand: 27
19	Operation	operator: 23 operand: 27
20	ExprTuple	28
21	Operation	operator: 25 operands: 26
22	Variable
23	Variable
24	ExprTuple	27
25	Variable
26	ExprTuple	27, 28
27	Variable
28	Variable