Expression of type Lambda

from the theory of proveit.numbers.divisibility

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, Lambda, p, x, y
from proveit.logic import And, InSet, Not
from proveit.numbers import Divides, NaturalPos, greater, one

# build up the expression from sub-expressions
expr = Lambda(p, Conditional(Not(And(Divides(p, x), Divides(p, y))), And(InSet(p, NaturalPos), greater(p, one))))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

p \mapsto \left\{\lnot \left(\left(p \rvert x\right) \land \left(p \rvert y\right)\right) \textrm{ if } p \in \mathbb{N}^+ ,  p > 1\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 25 body: 2
1	ExprTuple	25
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 11 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 15 operands: 16
11	Literal
12	ExprTuple	17, 18
13	Literal
14	ExprTuple	25, 19
15	Literal
16	ExprTuple	20, 25
17	Operation	operator: 22 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	25, 24
22	Literal
23	ExprTuple	25, 26
24	Variable
25	Variable
26	Variable