Expression of type Forall

from the theory of proveit.numbers.number_sets.real_numbers

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 a, b, x
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import IntervalOC, Less, LessEq, Real

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b], instance_expr = Forall(instance_param_or_params = [x], instance_expr = Equals(InSet(x, IntervalOC(a, b)), And(InSet(x, Real), And(Less(a, x), LessEq(x, b)).with_total_ordering_style()))), domain = Real)

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_{a, b \in \mathbb{R}}~\left[\forall_{x}~\left(\left(x \in \left(a,b\right]\right) = \left(\left(x \in \mathbb{R}\right) \land \left(a < x \leq b\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: 26 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 29 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameter: 39 body: 13
10	Operation	operator: 27 operands: 14
11	Operation	operator: 27 operands: 15
12	ExprTuple	39
13	Operation	operator: 16 operands: 17
14	ExprTuple	38, 31
15	ExprTuple	40, 31
16	Literal
17	ExprTuple	18, 19
18	Operation	operator: 27 operands: 20
19	Operation	operator: 29 operands: 21
20	ExprTuple	39, 22
21	ExprTuple	23, 24
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operands: 30
25	Literal
26	ExprTuple	38, 40
27	Literal
28	ExprTuple	39, 31
29	Literal
30	ExprTuple	32, 33
31	Literal
32	Operation	operator: 34 operands: 35
33	Operation	operator: 36 operands: 37
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	39, 40
38	Variable
39	Variable
40	Variable