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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 x
from proveit.logic import Equals, Forall
from proveit.numbers import Mult, Real, greater_eq, sqrt, zero
In [2]:
# build up the expression from sub-expressions
sub_expr1 = sqrt(x)
expr = Forall(instance_param_or_params = [x], instance_expr = Equals(Mult(sub_expr1, sub_expr1), x), domain = Real, condition = greater_eq(x, zero))
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_{x \in \mathbb{R}~|~x \geq 0}~\left(\left(\sqrt{x} \cdot \sqrt{x}\right) = x\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
3Lambdaparameter: 26
body: 5
4ExprTuple26
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12, 26
10Literal
11ExprTuple13, 14
12Operationoperator: 15
operands: 16
13Operationoperator: 17
operands: 18
14Operationoperator: 19
operands: 20
15Literal
16ExprTuple21, 21
17Literal
18ExprTuple26, 22
19Literal
20ExprTuple23, 26
21Operationoperator: 24
operands: 25
22Literal
23Literal
24Literal
25ExprTuple26, 27
26Variable
27Operationoperator: 28
operands: 29
28Literal
29ExprTuple30, 31
30Literal
31Literal