lean2/tests/lean/cast4.lean.expected.out
Leonardo de Moura 2b2aa228e3 refactor(builtin/kernel): start with small universes
The universe constraint manager is more flexible now.
We don't need to start with a huge universe  U >= 512.
We can start small, and increase it on demand.

If module mod1 needs it, it can always add

   universe U >= 3

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-08 12:35:00 -08:00

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Set: pp::colors
Set: pp::unicode
Imported 'cast'
Set: pp::colors
Defined: TypeM
λ (A A' : TypeM)
(B : A → TypeM)
(B' : A' → TypeM)
(f : ∀ x : A, B x)
(g : ∀ x : A', B' x)
(a : A)
(b : A')
(H1 : (∀ x : A, B x) == (∀ x : A', B' x))
(H2 : f == g)
(H3 : a == b),
let S1 : (∀ x : A', B' x) == (∀ x : A, B x) := symm H1,
L2 : A' == A := dominj S1,
b' : A := cast L2 b,
L3 : b == b' := cast::eq L2 b,
L4 : a == b' := htrans H3 L3,
L5 : f a == f b' := congr2 f L4,
g' : ∀ x : A, B x := cast S1 g,
L6 : g == g' := cast::eq S1 g,
L7 : f == g' := htrans H2 L6,
L8 : f b' == g' b' := congr1 b' L7,
L9 : f a == g' b' := htrans L5 L8,
L10 : g' b' == g b := cast::app S1 L2 g b
in htrans L9 L10 :
∀ (A A' : TypeM)
(B : A → TypeM)
(B' : A' → TypeM)
(f : ∀ x : A, B x)
(g : ∀ x : A', B' x)
(a : A)
(b : A'),
(∀ x : A, B x) == (∀ x : A', B' x) → f == g → a == b → f a == g b