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Expression of type And

from the theory of proveit.numbers.divisibility

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, y, z
from proveit.logic import And, Equals, InSet
from proveit.numbers import Divides, GCD, Integer, Mult, one
In [2]:
# build up the expression from sub-expressions
expr = And(InSet(x, Integer), InSet(y, Integer), InSet(z, Integer), Divides(x, Mult(y, z)), Equals(GCD(x, y), 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(x \in \mathbb{Z}\right) \land \left(y \in \mathbb{Z}\right) \land \left(z \in \mathbb{Z}\right) \land \left(x \rvert \left(y \cdot z\right)\right) \land \left(gcd\left(x, y\right) = 1\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, 6, 7
3Operationoperator: 10
operands: 8
4Operationoperator: 10
operands: 9
5Operationoperator: 10
operands: 11
6Operationoperator: 12
operands: 13
7Operationoperator: 14
operands: 15
8ExprTuple25, 16
9ExprTuple26, 16
10Literal
11ExprTuple24, 16
12Literal
13ExprTuple25, 17
14Literal
15ExprTuple18, 19
16Literal
17Operationoperator: 20
operands: 21
18Operationoperator: 22
operands: 23
19Literal
20Literal
21ExprTuple26, 24
22Literal
23ExprTuple25, 26
24Variable
25Variable
26Variable