from the theory of proveit.core_expr_types.tuples¶

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.
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, i, x
from proveit.core_expr_types import Len, f_1_to_i, range_1_to_ip1
from proveit.logic import Equals, InSet
from proveit.numbers import Natural

In [2]:
# build up the expression from sub-expressions
expr = Lambda(i, Conditional(Equals(Len(operands = [f_1_to_i, x]), Len(operands = [range_1_to_ip1])), InSet(i, Natural)))

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())

i \mapsto \left\{|\left(f\left(1\right), f\left(2\right), \ldots, f\left(i\right), x\right)| = |\left(1, 2, \ldots, \left(i + 1\right)\right)| \textrm{ if } i \in \mathbb{N}\right..

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameter: 26
body: 2
1ExprTuple26
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple26, 11
9Operationoperator: 13
operands: 12
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple15, 16
13Literal
14ExprTuple17
15ExprRangelambda_map: 18
start_index: 27
end_index: 26
16Variable
17ExprRangelambda_map: 19
start_index: 27
end_index: 20
18Lambdaparameter: 28
body: 21
19Lambdaparameter: 28
body: 28
20Operationoperator: 22
operands: 23
21Operationoperator: 24
operand: 28
22Literal
23ExprTuple26, 27
24Variable
25ExprTuple28
26Variable
27Literal
28Variable