Theorem tuple_portion_substitution 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 tuple_portion_substitution

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

Passed sanity check: tuple_portion_substitution matches stored_expr

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

\forall_{i, j, k \in \mathbb{N}}~\left[\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}, c_{1}, c_{2}, \ldots, c_{k}, d_{1}, d_{2}, \ldots, d_{j}~|~\left(b_{1}, b_{2}, \ldots, b_{j}\right) = \left(d_{1}, d_{2}, \ldots, d_{j}\right)}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1}, a_{2}, \ldots, a_{i},b_{1}, b_{2}, \ldots, b_{j},c_{1}, c_{2}, \ldots, c_{k}\right) =  \\ \left(a_{1}, a_{2}, \ldots, a_{i},d_{1}, d_{2}, \ldots, d_{j},c_{1}, c_{2}, \ldots, c_{k}\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	36, 42, 38
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	12, 13, 14
11	Lambda	parameters: 15 body: 16
12	Operation	operator: 19 operands: 17
13	Operation	operator: 19 operands: 18
14	Operation	operator: 19 operands: 20
15	ExprTuple	31, 33, 32, 34
16	Conditional	value: 21 condition: 22
17	ExprTuple	36, 23
18	ExprTuple	42, 23
19	Literal
20	ExprTuple	38, 23
21	Operation	operator: 25 operands: 24
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	29, 30
27	ExprTuple	31, 33, 32
28	ExprTuple	31, 34, 32
29	ExprTuple	33
30	ExprTuple	34
31	ExprRange	lambda_map: 35 start_index: 41 end_index: 36
32	ExprRange	lambda_map: 37 start_index: 41 end_index: 38
33	ExprRange	lambda_map: 39 start_index: 41 end_index: 42
34	ExprRange	lambda_map: 40 start_index: 41 end_index: 42
35	Lambda	parameter: 52 body: 43
36	Variable
37	Lambda	parameter: 52 body: 44
38	Variable
39	Lambda	parameter: 52 body: 45
40	Lambda	parameter: 52 body: 46
41	Literal
42	Variable
43	IndexedVar	variable: 47 index: 52
44	IndexedVar	variable: 48 index: 52
45	IndexedVar	variable: 49 index: 52
46	IndexedVar	variable: 50 index: 52
47	Variable
48	Variable
49	Variable
50	Variable
51	ExprTuple	52
52	Variable