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Expression of type ExprTuple

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 ExprTuple, S, x
from proveit.logic import Forall, InSet
from proveit.numbers import Add, one, zero
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(InSet(zero, S), Forall(instance_param_or_params = [x], instance_expr = InSet(Add(x, one), S), domain = S))
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(0 \in S, \forall_{x \in S}~\left(\left(x + 1\right) \in S\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
1Operationoperator: 13
operands: 3
2Operationoperator: 4
operand: 7
3ExprTuple6, 16
4Literal
5ExprTuple7
6Literal
7Lambdaparameter: 19
body: 9
8ExprTuple19
9Conditionalvalue: 10
condition: 11
10Operationoperator: 13
operands: 12
11Operationoperator: 13
operands: 14
12ExprTuple15, 16
13Literal
14ExprTuple19, 16
15Operationoperator: 17
operands: 18
16Variable
17Literal
18ExprTuple19, 20
19Variable
20Literal