Expression of type Forall

from the theory of proveit.numbers.addition

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 a, b, c, d
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Integer, Mult, frac

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, c, d], instance_expr = Equals(Add(frac(a, b), frac(c, d)), frac(Add(Mult(a, d), Mult(b, c)), Mult(b, d))), domain = Integer)

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 \in \mathbb{Z}}~\left(\left(\frac{a}{b} + \frac{c}{d}\right) = \frac{\left(a \cdot d\right) + \left(b \cdot c\right)}{b \cdot d}\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	41, 43, 44, 42
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15, 16, 17
12	Operation	operator: 33 operands: 18
13	Operation	operator: 31 operands: 19
14	Operation	operator: 23 operands: 20
15	Operation	operator: 23 operands: 21
16	Operation	operator: 23 operands: 22
17	Operation	operator: 23 operands: 24
18	ExprTuple	25, 26
19	ExprTuple	27, 28
20	ExprTuple	41, 29
21	ExprTuple	43, 29
22	ExprTuple	44, 29
23	Literal
24	ExprTuple	42, 29
25	Operation	operator: 31 operands: 30
26	Operation	operator: 31 operands: 32
27	Operation	operator: 33 operands: 34
28	Operation	operator: 39 operands: 35
29	Literal
30	ExprTuple	41, 43
31	Literal
32	ExprTuple	44, 42
33	Literal
34	ExprTuple	36, 37
35	ExprTuple	43, 42
36	Operation	operator: 39 operands: 38
37	Operation	operator: 39 operands: 40
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	43, 44
41	Variable
42	Variable
43	Variable
44	Variable