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 ExprRange, S, Variable, m
from proveit.logic import CartExp, CartProd, Equals, Forall
from proveit.numbers import one

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [S], instance_expr = Equals(CartExp(S, m), CartProd(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), S, one, m))))

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_{S}~\left(S^{m} = \left(S \times  S \times  ..\left(m - 3\right) \times.. \times  S\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: 19 body: 5
4	ExprTuple	19
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	19, 17
12	Literal
13	ExprTuple	14
14	ExprRange	lambda_map: 15 start_index: 16 end_index: 17
15	Lambda	parameter: 20 body: 19
16	Literal
17	Variable
18	ExprTuple	20
19	Variable
20	Variable