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Expression of type ExprTuple

from the theory of proveit.numbers.multiplication

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 Conditional, ExprTuple, Lambda, a, x, y
from proveit.logic import And, Equals, InSet
from proveit.numbers import Mult, Natural
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, x, y], Conditional(Equals(Mult(a, x), Mult(a, y)), And(InSet(a, Natural), InSet(x, Natural), InSet(y, Natural), Equals(x, y)))))
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(\left(a, x, y\right) \mapsto \left\{\left(a \cdot x\right) = \left(a \cdot y\right) \textrm{ if } a \in \mathbb{N} ,  x \in \mathbb{N} ,  y \in \mathbb{N} ,  x = y\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 2
body: 3
2ExprTuple24, 26, 27
3Conditionalvalue: 4
condition: 5
4Operationoperator: 22
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple9, 10
7Literal
8ExprTuple11, 12, 13, 14
9Operationoperator: 16
operands: 15
10Operationoperator: 16
operands: 17
11Operationoperator: 20
operands: 18
12Operationoperator: 20
operands: 19
13Operationoperator: 20
operands: 21
14Operationoperator: 22
operands: 23
15ExprTuple24, 26
16Literal
17ExprTuple24, 27
18ExprTuple24, 25
19ExprTuple26, 25
20Literal
21ExprTuple27, 25
22Literal
23ExprTuple26, 27
24Variable
25Literal
26Variable
27Variable