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Expression of type Forall

from the theory of proveit.numbers.number_sets.natural_numbers

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 m, n
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Natural, one
In [2]:
# build up the expression from sub-expressions
expr = Forall([m, n], Equals(n, m), domains = [Natural, Natural], condition = Equals(Add(m, one), Add(n, one)))
Out[2]:
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(expr.latex())
\forall_{m, n \in \mathbb{N}~|~\left(m + 1\right) = \left(n + 1\right)}~\left(n = m\right)
In [5]:
expr.style_options()
Out[5]:
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
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
expr.expr_info()
Out[6]:
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple25, 26
5Conditionalvalue: 6
condition: 7
6Operationoperator: 17
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple26, 25
9Literal
10ExprTuple11, 12, 13
11Operationoperator: 15
operands: 14
12Operationoperator: 15
operands: 16
13Operationoperator: 17
operands: 18
14ExprTuple25, 19
15Literal
16ExprTuple26, 19
17Literal
18ExprTuple20, 21
19Literal
20Operationoperator: 23
operands: 22
21Operationoperator: 23
operands: 24
22ExprTuple25, 27
23Literal
24ExprTuple26, 27
25Variable
26Variable
27Literal