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Revert 'chore(library/init/data/nat): backport Nat.le from Lean4 (#603)…
…' (#607) Daniel and Leo have decided to instead to try forward porting Lean3's `nat.le`, so in the meantime I think we should revert #603 to maintain compatibility with mathlib. :-) https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Nat.2Ele.20backport
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Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -1,7 +1,10 @@ | ||
namespace nat | ||
#check induction_on -- ERROR | ||
#check rec_on -- ERROR | ||
#check less_than_or_equal.rec_on -- OK | ||
#check nat.less_than_or_equal.rec_on | ||
namespace le | ||
#check rec_on -- ERROR | ||
#check less_than_or_equal.rec_on | ||
end le | ||
end nat |
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Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -1,3 +1,12 @@ | ||
protected_test.lean:2:9: error: unknown identifier 'induction_on' | ||
protected_test.lean:3:9: error: unknown identifier 'rec_on' | ||
protected_test.lean:5:11: error: unknown identifier 'rec_on' | ||
less_than_or_equal.rec_on : | ||
?M_1.less_than_or_equal ?M_3 → | ||
?M_2 ?M_1 → (∀ {b : ℕ}, ?M_1.less_than_or_equal b → ?M_2 b → ?M_2 b.succ) → ?M_2 ?M_3 | ||
less_than_or_equal.rec_on : | ||
?M_1.less_than_or_equal ?M_3 → | ||
?M_2 ?M_1 → (∀ {b : ℕ}, ?M_1.less_than_or_equal b → ?M_2 b → ?M_2 b.succ) → ?M_2 ?M_3 | ||
protected_test.lean:7:11: error: unknown identifier 'rec_on' | ||
less_than_or_equal.rec_on : | ||
?M_1.less_than_or_equal ?M_3 → | ||
?M_2 ?M_1 → (∀ {b : ℕ}, ?M_1.less_than_or_equal b → ?M_2 b → ?M_2 b.succ) → ?M_2 ?M_3 |
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Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -1,8 +1,8 @@ | ||
open nat | ||
|
||
definition not_false' (a : nat) : ¬ false := | ||
assume H : false, | ||
definition not_lt_zero (a : nat) : ¬ a < 0 := | ||
assume H : a < 0, | ||
match H with | ||
end | ||
|
||
#check _root_.not_false' | ||
#check _root_.not_lt_zero |
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