Expression of type Forall

from the theory of proveit.numbers.numerals.decimals

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 import Function, f, i, j
from proveit.core_expr_types import f_i_to_j
from proveit.logic import Equals, Forall
from proveit.numbers import Add, one, two

# build up the expression from sub-expressions
sub_expr1 = Add(i, two)
expr = Forall(instance_param_or_params = [f, i, j], instance_expr = Equals([f_i_to_j], [Function(f, [i]), Function(f, [Add(i, one)]), Function(f, [sub_expr1])]), condition = Equals(j, sub_expr1))

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_{f, i, j~|~j = \left(i + 2\right)}~\left(\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right) = \left(f\left(i\right), f\left(i + 1\right), f\left(i + 2\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	25, 32, 18
5	Conditional	value: 6 condition: 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	18, 24
11	ExprTuple	13
12	ExprTuple	14, 15, 16
13	ExprRange	lambda_map: 17 start_index: 32 end_index: 18
14	Operation	operator: 25 operand: 32
15	Operation	operator: 25 operand: 23
16	Operation	operator: 25 operand: 24
17	Lambda	parameter: 30 body: 22
18	Variable
19	ExprTuple	32
20	ExprTuple	23
21	ExprTuple	24
22	Operation	operator: 25 operand: 30
23	Operation	operator: 28 operands: 27
24	Operation	operator: 28 operands: 29
25	Variable
26	ExprTuple	30
27	ExprTuple	32, 31
28	Literal
29	ExprTuple	32, 33
30	Variable
31	Literal
32	Variable
33	Literal