Theorem skolem_elim_lemma of type Forall

from the theory of proveit.logic.booleans.quantification.existence

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.booleans.quantification.existence import skolem_elim_lemma

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

Passed sanity check: skolem_elim_lemma 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}^+, \alpha \in \mathbb{B}}~\left[\forall_{P, Q}~\left(\left(\left[\exists_{y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right] \land \left[\forall_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~\left(P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \Rightarrow \alpha\right)\right]\right) \Rightarrow \alpha\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: 27 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	52, 43
4	Conditional	value: 5 condition: 6
5	Operation	operator: 27 operand: 9
6	Operation	operator: 21 operands: 8
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 12 body: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	45, 40
13	Operation	operator: 38 operands: 17
14	ExprTuple	52, 18
15	Literal
16	ExprTuple	43, 19
17	ExprTuple	20, 43
18	Literal
19	Literal
20	Operation	operator: 21 operands: 22
21	Literal
22	ExprTuple	23, 24
23	Operation	operator: 25 operand: 29
24	Operation	operator: 27 operand: 30
25	Literal
26	ExprTuple	29
27	Literal
28	ExprTuple	30
29	Lambda	parameters: 37 body: 31
30	Lambda	parameters: 46 body: 32
31	Conditional	value: 33 condition: 34
32	Conditional	value: 35 condition: 36
33	Operation	operator: 45 operands: 37
34	Operation	operator: 40 operands: 37
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operands: 46
37	ExprTuple	41
38	Literal
39	ExprTuple	42, 43
40	Variable
41	ExprRange	lambda_map: 44 start_index: 51 end_index: 52
42	Operation	operator: 45 operands: 46
43	Variable
44	Lambda	parameter: 56 body: 47
45	Variable
46	ExprTuple	48
47	IndexedVar	variable: 49 index: 56
48	ExprRange	lambda_map: 50 start_index: 51 end_index: 52
49	Variable
50	Lambda	parameter: 56 body: 53
51	Literal
52	Variable
53	IndexedVar	variable: 54 index: 56
54	Variable
55	ExprTuple	56
56	Variable