Expression of type Forall

from the theory of proveit.numbers.exponentiation

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, NotEquals
from proveit.numbers import Add, Exp, Integer, Mult, Real, zero

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, c, d], instance_expr = Equals(Exp(a, b), Mult(Exp(a, c), Exp(a, d))), domains = [Real, Integer, Integer, Integer], conditions = [NotEquals(a, zero), Equals(b, Add(c, d))])

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 \in \mathbb{R}, b \in \mathbb{Z}, c \in \mathbb{Z}, d \in \mathbb{Z}~|~a \neq 0, b = \left(c + d\right)}~\left(a^{b} = \left(a^{c} \cdot a^{d}\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	43, 36, 44, 45
5	Conditional	value: 6 condition: 7
6	Operation	operator: 29 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14, 15, 16, 17, 18
11	Operation	operator: 39 operands: 19
12	Operation	operator: 20 operands: 21
13	Operation	operator: 25 operands: 22
14	Operation	operator: 25 operands: 23
15	Operation	operator: 25 operands: 24
16	Operation	operator: 25 operands: 26
17	Operation	operator: 27 operands: 28
18	Operation	operator: 29 operands: 30
19	ExprTuple	43, 36
20	Literal
21	ExprTuple	31, 32
22	ExprTuple	43, 33
23	ExprTuple	36, 34
24	ExprTuple	44, 34
25	Literal
26	ExprTuple	45, 34
27	Literal
28	ExprTuple	43, 35
29	Literal
30	ExprTuple	36, 37
31	Operation	operator: 39 operands: 38
32	Operation	operator: 39 operands: 40
33	Literal
34	Literal
35	Literal
36	Variable
37	Operation	operator: 41 operands: 42
38	ExprTuple	43, 44
39	Literal
40	ExprTuple	43, 45
41	Literal
42	ExprTuple	44, 45
43	Variable
44	Variable
45	Variable