Theorem sub_in_left_operands_via_tuple of type Forall

from the theory of proveit.logic.equality

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.logic.equality import sub_in_left_operands_via_tuple

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

Passed sanity check: sub_in_left_operands_via_tuple matches stored_expr

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

\forall_{n \in \mathbb{N}}~\left[\forall_{P, x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}~|~P\left(y_{1}, y_{2}, \ldots, y_{n}\right), \left(x_{1}, x_{2}, \ldots, x_{n}\right) = \left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\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	parameter: 31 body: 4
3	ExprTuple	31
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	31, 12
11	Lambda	parameters: 13 body: 14
12	Literal
13	ExprTuple	21, 26, 27
14	Conditional	value: 15 condition: 16
15	Operation	operator: 21 operands: 24
16	Operation	operator: 17 operands: 18
17	Literal
18	ExprTuple	19, 20
19	Operation	operator: 21 operands: 25
20	Operation	operator: 22 operands: 23
21	Variable
22	Literal
23	ExprTuple	24, 25
24	ExprTuple	26
25	ExprTuple	27
26	ExprRange	lambda_map: 28 start_index: 30 end_index: 31
27	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
28	Lambda	parameter: 37 body: 32
29	Lambda	parameter: 37 body: 33
30	Literal
31	Variable
32	IndexedVar	variable: 34 index: 37
33	IndexedVar	variable: 35 index: 37
34	Variable
35	Variable
36	ExprTuple	37
37	Variable