Expression of type Forall

from the theory of proveit.numbers.numerals.decimals

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, Variable, a, b, c, d, e, f, g, h, i
from proveit.core_expr_types import Len
from proveit.logic import Equals, Forall
from proveit.numbers import nine, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [a, b, c, d, e, f, g, h, i]
expr = Forall(instance_param_or_params = sub_expr2, instance_expr = Equals(Len(operands = sub_expr2), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, nine)])))

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, c, d, e, f, g, h, i}~\left(|\left(a, b, c, d, e, f, g, h, i\right)| = |\left(1, 2, \ldots, 9\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	parameters: 9 body: 4
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8
7	Operation	operator: 10 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	12, 13, 14, 15, 16, 17, 18, 19, 20
10	Literal
11	ExprTuple	21
12	Variable
13	Variable
14	Variable
15	Variable
16	Variable
17	Variable
18	Variable
19	Variable
20	Variable
21	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
22	Lambda	parameter: 26 body: 26
23	Literal
24	Literal
25	ExprTuple	26
26	Variable