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Expression of type Forall

from the theory of proveit.numbers.exponentiation

In [1]:
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
In [2]:
# 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:
In [3]:
# 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
In [4]:
# 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)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple43, 36, 44, 45
5Conditionalvalue: 6
condition: 7
6Operationoperator: 29
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 12
9Literal
10ExprTuple13, 14, 15, 16, 17, 18
11Operationoperator: 39
operands: 19
12Operationoperator: 20
operands: 21
13Operationoperator: 25
operands: 22
14Operationoperator: 25
operands: 23
15Operationoperator: 25
operands: 24
16Operationoperator: 25
operands: 26
17Operationoperator: 27
operands: 28
18Operationoperator: 29
operands: 30
19ExprTuple43, 36
20Literal
21ExprTuple31, 32
22ExprTuple43, 33
23ExprTuple36, 34
24ExprTuple44, 34
25Literal
26ExprTuple45, 34
27Literal
28ExprTuple43, 35
29Literal
30ExprTuple36, 37
31Operationoperator: 39
operands: 38
32Operationoperator: 39
operands: 40
33Literal
34Literal
35Literal
36Variable
37Operationoperator: 41
operands: 42
38ExprTuple43, 44
39Literal
40ExprTuple43, 45
41Literal
42ExprTuple44, 45
43Variable
44Variable
45Variable