Theorem merge_series of type Forall

from the theory of proveit.core_expr_types.tuples

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.core_expr_types.tuples import merge_series

# check that the built expression is the same as the stored expression
assert merge_series.expr == stored_expr
assert merge_series.expr._style_id == stored_expr._style_id
print("Passed sanity check: merge_series matches stored_expr")

Passed sanity check: merge_series 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(j - i\right) \in \mathbb{N}}~\left[\forall_{x_{0}, x_{1}, \ldots, x_{j - i}~|~\left(x_{0} = f\left(i + 0\right)\right), \left(x_{1} = f\left(i + 1\right)\right), \ldots, \left(x_{j - i} = f\left(i + \left(j - i\right)\right)\right)}~\left(\begin{array}{c} \begin{array}{l} \left(x_{0}, x_{1}, \ldots, x_{j - i}\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right) \end{array} \end{array}\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	42, 47, 34
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	27, 12
11	Lambda	parameters: 19 body: 13
12	Literal
13	Conditional	value: 14 condition: 15
14	Operation	operator: 32 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21
19	ExprTuple	22
20	ExprTuple	23
21	ExprRange	lambda_map: 24 start_index: 26 end_index: 27
22	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
23	ExprRange	lambda_map: 28 start_index: 47 end_index: 34
24	Lambda	parameter: 48 body: 29
25	Lambda	parameter: 48 body: 36
26	Literal
27	Operation	operator: 45 operands: 30
28	Lambda	parameter: 48 body: 31
29	Operation	operator: 32 operands: 33
30	ExprTuple	34, 35
31	Operation	operator: 42 operand: 48
32	Literal
33	ExprTuple	36, 37
34	Variable
35	Operation	operator: 38 operand: 47
36	IndexedVar	variable: 40 index: 48
37	Operation	operator: 42 operand: 44
38	Literal
39	ExprTuple	47
40	Variable
41	ExprTuple	48
42	Variable
43	ExprTuple	44
44	Operation	operator: 45 operands: 46
45	Literal
46	ExprTuple	47, 48
47	Variable
48	Variable