Expression of type Forall

from the theory of proveit.numbers.functions

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 Conditional, ConditionalSet, i, j
from proveit.logic import Equals, Forall, NotEquals
from proveit.numbers import KroneckerDelta, one, zero

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [i, j], instance_expr = Equals(KroneckerDelta(i, j), ConditionalSet(Conditional(one, Equals(i, j)), Conditional(zero, NotEquals(i, j)))))

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_{i, j}~\left(\delta_{i, j} = \left\{\begin{array}{ccc}1 \textrm{ if } i = j \\ 0 \textrm{ if } i \neq j\end{array}\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: 19 body: 4
4	Operation	operator: 17 operands: 5
5	ExprTuple	6, 7
6	Operation	operator: 8 operands: 19
7	Operation	operator: 9 operands: 10
8	Literal
9	Literal
10	ExprTuple	11, 12
11	Conditional	value: 13 condition: 14
12	Conditional	value: 15 condition: 16
13	Literal
14	Operation	operator: 17 operands: 19
15	Literal
16	Operation	operator: 18 operands: 19
17	Literal
18	Literal
19	ExprTuple	20, 21
20	Variable
21	Variable