Theorem quantification_from_disjunction of type Forall

from the theory of proveit.logic.booleans.disjunction

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.disjunction import quantification_from_disjunction

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

Passed sanity check: quantification_from_disjunction matches stored_expr

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

\forall_{i, j \in \mathbb{Z}}~\left[\forall_{P}~\left(\left(P\left(i\right) \lor  P\left(i + 1\right) \lor  \ldots \lor  P\left(j\right)\right) \Rightarrow \left[\exists_{k \in \{i~\ldotp \ldotp~j\}}~P\left(k\right)\right]\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: 6 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 42 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11, 12
10	Lambda	parameter: 34 body: 14
11	Operation	operator: 36 operands: 15
12	Operation	operator: 36 operands: 16
13	ExprTuple	34
14	Operation	operator: 17 operands: 18
15	ExprTuple	43, 19
16	ExprTuple	44, 19
17	Literal
18	ExprTuple	20, 21
19	Literal
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operand: 27
22	Literal
23	ExprTuple	26
24	Literal
25	ExprTuple	27
26	ExprRange	lambda_map: 28 start_index: 43 end_index: 44
27	Lambda	parameter: 39 body: 29
28	Lambda	parameter: 38 body: 30
29	Conditional	value: 31 condition: 32
30	Operation	operator: 34 operand: 38
31	Operation	operator: 34 operand: 39
32	Operation	operator: 36 operands: 37
33	ExprTuple	38
34	Variable
35	ExprTuple	39
36	Literal
37	ExprTuple	39, 40
38	Variable
39	Variable
40	Operation	operator: 41 operands: 42
41	Literal
42	ExprTuple	43, 44
43	Variable
44	Variable