Expression of type Forall

from the theory of proveit.core_expr_types.tuples

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit.core_expr_types import merge_series_conditions, merge_series_equiv, x_0_to_jmi
from proveit.logic import Forall

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x_0_to_jmi], instance_expr = merge_series_equiv, condition = merge_series_conditions)

expr:

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

Passed sanity check: expr matches stored_expr

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

\forall_{x_{0}, x_{1}, \ldots, x_{j - i}~|~\left(x_{0} = f\left(i + 0\right)\right), \left(x_{1} = f\left(i + 1\right)\right), \ldots, \left(x_{j - i} = f\left(i + \left(j - i\right)\right)\right)}~\left(\begin{array}{c} \begin{array}{l} \left(x_{0}, x_{1}, \ldots, x_{j - i}\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 10 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 23 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12
10	ExprTuple	13
11	ExprTuple	14
12	ExprRange	lambda_map: 15 start_index: 17 end_index: 18
13	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
14	ExprRange	lambda_map: 19 start_index: 38 end_index: 25
15	Lambda	parameter: 39 body: 20
16	Lambda	parameter: 39 body: 27
17	Literal
18	Operation	operator: 36 operands: 21
19	Lambda	parameter: 39 body: 22
20	Operation	operator: 23 operands: 24
21	ExprTuple	25, 26
22	Operation	operator: 33 operand: 39
23	Literal
24	ExprTuple	27, 28
25	Variable
26	Operation	operator: 29 operand: 38
27	IndexedVar	variable: 31 index: 39
28	Operation	operator: 33 operand: 35
29	Literal
30	ExprTuple	38
31	Variable
32	ExprTuple	39
33	Variable
34	ExprTuple	35
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	38, 39
38	Variable
39	Variable