Expression of type ExprTuple

from the theory of proveit.core_expr_types.conditionals

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, m, n
from proveit.core_expr_types import Q_1_to_m, R_1_to_n
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, n], Conditional(Forall(instance_param_or_params = [a, Q_1_to_m, R_1_to_n], instance_expr = Equals(Conditional(a, And(And(Q_1_to_m), And(R_1_to_n))), Conditional(a, And(Q_1_to_m, R_1_to_n))).with_wrapping_at(1)), And(InSet(m, Natural), InSet(n, Natural)))))

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())

\left(\left(m, n\right) \mapsto \left\{\forall_{a, Q_{1}, Q_{2}, \ldots, Q_{m}, R_{1}, R_{2}, \ldots, R_{n}}~\left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q_{1} \land  Q_{2} \land  \ldots \land  Q_{m} ,  R_{1} \land  R_{2} \land  \ldots \land  R_{n}\right.. \\  = \left\{a \textrm{ if } Q_{1} ,  Q_{2} ,  \ldots ,  Q_{m}, R_{1} ,  R_{2} ,  \ldots ,  R_{n}\right.. \end{array} \end{array}\right) \textrm{ if } m \in \mathbb{N} ,  n \in \mathbb{N}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	35, 38
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 30 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 12 body: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	23, 32, 33
13	Operation	operator: 17 operands: 18
14	ExprTuple	35, 19
15	Literal
16	ExprTuple	38, 19
17	Literal
18	ExprTuple	20, 21
19	Literal
20	Conditional	value: 23 condition: 22
21	Conditional	value: 23 condition: 24
22	Operation	operator: 30 operands: 25
23	Variable
24	Operation	operator: 30 operands: 26
25	ExprTuple	27, 28
26	ExprTuple	32, 33
27	Operation	operator: 30 operands: 29
28	Operation	operator: 30 operands: 31
29	ExprTuple	32
30	Literal
31	ExprTuple	33
32	ExprRange	lambda_map: 34 start_index: 37 end_index: 35
33	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
34	Lambda	parameter: 44 body: 39
35	Variable
36	Lambda	parameter: 44 body: 40
37	Literal
38	Variable
39	IndexedVar	variable: 41 index: 44
40	IndexedVar	variable: 42 index: 44
41	Variable
42	Variable
43	ExprTuple	44
44	Variable