Expression of type Lambda

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, Lambda, Q, a, b
from proveit.logic import Equals, Implies

# build up the expression from sub-expressions
expr = Lambda([a, b, Q], Conditional(Equals(Conditional(a, Q), Conditional(b, Q)).with_wrapping_at(1), Implies(Q, Equals(a, b))))

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(a, b, Q\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q\right.. \\  = \left\{b \textrm{ if } Q\right.. \end{array} \end{array} \textrm{ if } Q \Rightarrow \left(a = b\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	14, 15, 11
2	Conditional	value: 3 condition: 4
3	Operation	operator: 12 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	11, 10
8	Conditional	value: 14 condition: 11
9	Conditional	value: 15 condition: 11
10	Operation	operator: 12 operands: 13
11	Variable
12	Literal
13	ExprTuple	14, 15
14	Variable
15	Variable