Theorem merge 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

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

Passed sanity check: merge matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

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