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 IntervalCO, Less, LessEq, Real

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

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}~\left(\left(x \in \left[a,b\right)\right) = \left(\left(x \in \mathbb{R}\right) \land \left(a \leq x < b\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: 29 body: 5
4	ExprTuple	29
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 17 operands: 10
9	Operation	operator: 19 operands: 11
10	ExprTuple	29, 12
11	ExprTuple	13, 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 19 operands: 20
15	Literal
16	ExprTuple	28, 30
17	Literal
18	ExprTuple	29, 21
19	Literal
20	ExprTuple	22, 23
21	Literal
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	29, 30
28	Variable
29	Variable
30	Variable