Expression of type Forall

from the theory of proveit.core_expr_types.tuples

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 f, i
from proveit.core_expr_types import Len, f_1_to_i
from proveit.logic import Equals, Forall

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f], instance_expr = Equals(Len(operands = [f_1_to_i]), i))

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_{f}~\left(|\left(f\left(1\right), f\left(2\right), \ldots, f\left(i\right)\right)| = i\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: 16 body: 5
4	ExprTuple	16
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 14
8	Operation	operator: 9 operands: 10
9	Literal
10	ExprTuple	11
11	ExprRange	lambda_map: 12 start_index: 13 end_index: 14
12	Lambda	parameter: 18 body: 15
13	Literal
14	Variable
15	Operation	operator: 16 operand: 18
16	Variable
17	ExprTuple	18
18	Variable