lean2/tests/lean/tactic4.lean.expected.out
Leonardo de Moura 20a36e98ec feat(library/elaborator): modify how elaborator handles constraints of the form ?M << P and P << ?M, where P is a proposition.
Before this commit, the elaborator would only assign ?M <- P, if P was normalized. This is bad since normalization may "destroy" the structure of P.

For example, consider the constraint
[a : Bool; b : Bool; c : Bool] ⊢ ?M::1 ≺ implies a (implies b (and a b))

Before this, ?M::1 will not be assigned to the "implies-term" because the "implies-term" is not normalized yet.
So, the elaborator would continue to process the constraint, and convert it into:

[a : Bool; b : Bool; c : Bool] ⊢ ?M::1 ≺ if Bool a (if Bool b (if Bool (if Bool a (if Bool b false true) true) false true) true) true

Now, ?M::1 is assigned to the term
     if Bool a (if Bool b (if Bool (if Bool a (if Bool b false true) true) false true) true) true

This is bad, since the original structure was lost.

This commit also contains an example that only works after the commit is applied.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2013-11-29 09:15:01 -08:00

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Set: pp::colors
Set: pp::unicode
Proved: T4
Theorem T4 (a b : Bool) : a ⇒ b ⇒ a ∧ b := Discharge (λ H : a, Discharge (λ H::1 : b, Conj H H::1))