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Expression of type ExprTuple

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 ExprTuple, a_star, b_star
from proveit.logic import And, Equals, InSet
from proveit.numbers import Abs, GCD, NaturalPos, frac, one, sqrt, two
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(InSet(a_star, NaturalPos), InSet(b_star, NaturalPos), And(Equals(Abs(sqrt(two)), frac(a_star, b_star)), Equals(GCD(a_star, b_star), 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(a^* \in \mathbb{N}^+, b^* \in \mathbb{N}^+, \left(\left|\sqrt{2}\right| = \frac{a^*}{b^*}\right) \land \left(gcd\left(a^*, b^*\right) = 1\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1, 2, 3
1Operationoperator: 5
operands: 4
2Operationoperator: 5
operands: 6
3Operationoperator: 7
operands: 8
4ExprTuple23, 9
5Literal
6ExprTuple24, 9
7Literal
8ExprTuple10, 11
9Literal
10Operationoperator: 13
operands: 12
11Operationoperator: 13
operands: 14
12ExprTuple15, 16
13Literal
14ExprTuple17, 30
15Operationoperator: 18
operand: 22
16Operationoperator: 28
operands: 21
17Operationoperator: 20
operands: 21
18Literal
19ExprTuple22
20Literal
21ExprTuple23, 24
22Operationoperator: 25
operands: 26
23Variable
24Variable
25Literal
26ExprTuple31, 27
27Operationoperator: 28
operands: 29
28Literal
29ExprTuple30, 31
30Literal
31Literal