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Expression of type And

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 And, Equals, InSet
from proveit.numbers import Add, Natural, one
In [2]:
# build up the expression from sub-expressions
expr = And(InSet(m, Natural), InSet(n, Natural), Equals(Add(m, one), Add(n, one)))
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())
\left(m \in \mathbb{N}\right) \land \left(n \in \mathbb{N}\right) \land \left(\left(m + 1\right) = \left(n + 1\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4, 5
3Operationoperator: 7
operands: 6
4Operationoperator: 7
operands: 8
5Operationoperator: 9
operands: 10
6ExprTuple17, 11
7Literal
8ExprTuple18, 11
9Literal
10ExprTuple12, 13
11Literal
12Operationoperator: 15
operands: 14
13Operationoperator: 15
operands: 16
14ExprTuple17, 19
15Literal
16ExprTuple18, 19
17Variable
18Variable
19Literal