Expression of type Forall

from the theory of proveit.logic.booleans.disjunction

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 ExprRange, Function, P, Pk, Variable, i, j, k
from proveit.logic import Exists, Forall, Implies, Or
from proveit.numbers import Interval

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [P], instance_expr = Implies(Or(ExprRange(sub_expr1, Function(P, [sub_expr1]), i, j)), Exists(instance_param_or_params = [k], instance_expr = Pk, domain = Interval(i, j))))

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_{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)

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	parameter: 22 body: 5
4	ExprTuple	22
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operand: 15
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	15
14	ExprRange	lambda_map: 16 start_index: 31 end_index: 32
15	Lambda	parameter: 27 body: 17
16	Lambda	parameter: 26 body: 18
17	Conditional	value: 19 condition: 20
18	Operation	operator: 22 operand: 26
19	Operation	operator: 22 operand: 27
20	Operation	operator: 24 operands: 25
21	ExprTuple	26
22	Variable
23	ExprTuple	27
24	Literal
25	ExprTuple	27, 28
26	Variable
27	Variable
28	Operation	operator: 29 operands: 30
29	Literal
30	ExprTuple	31, 32
31	Variable
32	Variable