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.core_expr_types import Len, f_1_to_n, i_1_to_n, j_1_to_n
from proveit.core_expr_types.tuples import f_ik_to_jk__1_to_n, range_len_conditions, range_len_sum
from proveit.logic import Equals, Forall

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f_1_to_n, i_1_to_n, j_1_to_n], instance_expr = Equals(Len(operands = [f_ik_to_jk__1_to_n]), range_len_sum).with_wrapping_at(1), condition = range_len_conditions).with_wrapping()

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())

\begin{array}{l}\forall_{f_{1}, f_{2}, \ldots, f_{n}, i_{1}, i_{2}, \ldots, i_{n}, j_{1}, j_{2}, \ldots, j_{n}~|~\left(\left(j_{1} - i_{1} + 1\right) \in \mathbb{N}\right), \left(\left(j_{2} - i_{2} + 1\right) \in \mathbb{N}\right), \ldots, \left(\left(j_{n} - i_{n} + 1\right) \in \mathbb{N}\right)}~\\
\left(\begin{array}{c} \begin{array}{l} |\left(f_{1}\left(i_{1}\right), f_{1}\left(i_{1} + 1\right), \ldots, f_{1}\left(j_{1}\right), f_{2}\left(i_{2}\right), f_{2}\left(i_{2} + 1\right), \ldots, f_{2}\left(j_{2}\right), \ldots\ldots, f_{n}\left(i_{n}\right), f_{n}\left(i_{n} + 1\right), \ldots, f_{n}\left(j_{n}\right)\right)| \\  = \left(\left(j_{1} - i_{1} + 1\right) +  \left(j_{2} - i_{2} + 1\right) +  \ldots +  \left(j_{n} - i_{n} + 1\right)\right) \end{array} \end{array}\right)\end{array}

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	True	('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	6, 7, 8
5	Conditional	value: 9 condition: 10
6	ExprRange	lambda_map: 11 start_index: 45 end_index: 31
7	ExprRange	lambda_map: 12 start_index: 45 end_index: 31
8	ExprRange	lambda_map: 13 start_index: 45 end_index: 31
9	Operation	operator: 14 operands: 15
10	Operation	operator: 16 operands: 17
11	Lambda	parameter: 56 body: 18
12	Lambda	parameter: 56 body: 52
13	Lambda	parameter: 56 body: 43
14	Literal
15	ExprTuple	19, 20
16	Literal
17	ExprTuple	21
18	IndexedVar	variable: 50 index: 56
19	Operation	operator: 22 operands: 23
20	Operation	operator: 40 operands: 24
21	ExprRange	lambda_map: 25 start_index: 45 end_index: 31
22	Literal
23	ExprTuple	26
24	ExprTuple	27
25	Lambda	parameter: 56 body: 28
26	ExprRange	lambda_map: 29 start_index: 45 end_index: 31
27	ExprRange	lambda_map: 30 start_index: 45 end_index: 31
28	Operation	operator: 32 operands: 33
29	Lambda	parameter: 53 body: 34
30	Lambda	parameter: 56 body: 35
31	Variable
32	Literal
33	ExprTuple	35, 36
34	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
35	Operation	operator: 40 operands: 41
36	Literal
37	Lambda	parameter: 56 body: 42
38	IndexedVar	variable: 54 index: 53
39	IndexedVar	variable: 47 index: 53
40	Literal
41	ExprTuple	43, 44, 45
42	Operation	operator: 46 operand: 56
43	IndexedVar	variable: 47 index: 56
44	Operation	operator: 48 operand: 52
45	Literal
46	IndexedVar	variable: 50 index: 53
47	Variable
48	Literal
49	ExprTuple	52
50	Variable
51	ExprTuple	53
52	IndexedVar	variable: 54 index: 56
53	Variable
54	Variable
55	ExprTuple	56
56	Variable