Expression of type Forall

from the theory of proveit.logic.sets.cartesian_products

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 S, m, x, y
from proveit.logic import Boolean, CartExp, Forall, InSet
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m], instance_expr = Forall(instance_param_or_params = [x, S], instance_expr = InSet(InSet(x, CartExp(S, m)), Boolean), condition = Forall(instance_param_or_params = [y], instance_expr = InSet(InSet(y, S), Boolean))), domain = NaturalPos)

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_{m \in \mathbb{N}^+}~\left[\forall_{x, S~|~\forall_{y}~\left(\left(y \in S\right) \in \mathbb{B}\right)}~\left(\left(x \in S^{m}\right) \in \mathbb{B}\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: 16 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 30 body: 4
3	ExprTuple	30
4	Conditional	value: 5 condition: 6
5	Operation	operator: 16 operand: 9
6	Operation	operator: 31 operands: 8
7	ExprTuple	9
8	ExprTuple	30, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	23, 34
12	Conditional	value: 13 condition: 14
13	Operation	operator: 31 operands: 15
14	Operation	operator: 16 operand: 19
15	ExprTuple	18, 29
16	Literal
17	ExprTuple	19
18	Operation	operator: 31 operands: 20
19	Lambda	parameter: 33 body: 22
20	ExprTuple	23, 24
21	ExprTuple	33
22	Operation	operator: 31 operands: 25
23	Variable
24	Operation	operator: 26 operands: 27
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	34, 30
28	Operation	operator: 31 operands: 32
29	Literal
30	Variable
31	Literal
32	ExprTuple	33, 34
33	Variable
34	Variable