Theorem forall_induction of type Forall

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

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.universality import forall_induction

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

Passed sanity check: forall_induction matches stored_expr

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

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