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Expression of type Forall

from the theory of proveit.numbers.modular

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 N, a, b
from proveit.logic import Forall
from proveit.numbers import ModAbs, Real, RealPos, greater_eq, subtract
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, N], instance_expr = greater_eq(ModAbs(subtract(a, b), N), subtract(ModAbs(a, N), ModAbs(b, N))), domains = [Real, Real, RealPos])
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{R}, N \in \mathbb{R}^+}~\left(\left|a - b\right|_{\textup{mod}\thinspace N} \geq \left(\left|a\right|_{\textup{mod}\thinspace N} - \left|b\right|_{\textup{mod}\thinspace N}\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
4ExprTuple33, 40, 39
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12, 13
10Literal
11ExprTuple14, 15, 16
12Operationoperator: 30
operands: 17
13Operationoperator: 35
operands: 18
14Operationoperator: 21
operands: 19
15Operationoperator: 21
operands: 20
16Operationoperator: 21
operands: 22
17ExprTuple23, 24
18ExprTuple25, 39
19ExprTuple33, 26
20ExprTuple40, 26
21Literal
22ExprTuple39, 27
23Operationoperator: 35
operands: 28
24Operationoperator: 37
operand: 32
25Operationoperator: 30
operands: 31
26Literal
27Literal
28ExprTuple33, 39
29ExprTuple32
30Literal
31ExprTuple33, 34
32Operationoperator: 35
operands: 36
33Variable
34Operationoperator: 37
operand: 40
35Literal
36ExprTuple40, 39
37Literal
38ExprTuple40
39Variable
40Variable