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 ExprRange, Function, Variable, f, i, j, m, n
from proveit.logic import Equals, Forall
from proveit.numbers import Add, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [f, i, j, m, n], instance_expr = Equals([ExprRange(sub_expr1, ExprRange(sub_expr2, Function(f, [sub_expr1, sub_expr2]), i, j), m, n)], []), condition = Equals(Add(n, 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_{f, i, j, m, n~|~\left(n + 1\right) = m}~\left(\left(f\left(m, i\right), f\left(m, i + 1\right), \ldots, f\left(m, j\right), f\left(m + 1, i\right), f\left(m + 1, i + 1\right), \ldots, f\left(m + 1, j\right), \ldots\ldots, f\left(n, i\right), f\left(n, i + 1\right), \ldots, f\left(n, j\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	parameters: 4 body: 5
4	ExprTuple	28, 24, 25, 18, 19
5	Conditional	value: 6 condition: 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 18
11	ExprTuple	14
12	ExprTuple
13	Operation	operator: 15 operands: 16
14	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
15	Literal
16	ExprTuple	19, 20
17	Lambda	parameter: 30 body: 22
18	Variable
19	Variable
20	Literal
21	ExprTuple	30
22	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
23	Lambda	parameter: 31 body: 27
24	Variable
25	Variable
26	ExprTuple	31
27	Operation	operator: 28 operands: 29
28	Variable
29	ExprTuple	30, 31
30	Variable
31	Variable