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fix(library/data/finset/equiv): broken proof

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TODO: investigate why the proof has to be fixed
This commit is contained in:
Leonardo de Moura 2015-09-11 23:24:29 -07:00
parent de2906ee8e
commit e9809a453d
1 changed files with 7 additions and 7 deletions
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14
library/data/finset/equiv.lean
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@ -145,22 +145,22 @@ private lemma of_nat_eq_insert : ∀ {n s : nat}, n ∉ of_nat s → of_nat (2^n
have gen : ∀ m, m ∈ of_nat (2^(succ n) + s) ↔ m ∈ insert (succ n) (of_nat s)
| zero :=
have even (2^(succ n)), by rewrite [pow_succ', mul.comm]; apply even_two_mul,
have aux₁ : odd (2^(succ n) + s) ↔ odd s, from iff.intro
assert aux₁ : odd (2^(succ n) + s) ↔ odd s, from iff.intro
(suppose odd (2^(succ n) + s), by_contradiction
(suppose ¬ odd s,
have even s, from even_of_not_odd this,
have even (2^(succ n) + s), from even_add_of_even_of_even `even (2^(succ n))` this,
absurd `odd (2^(succ n) + s)` (not_odd_of_even this)))
(suppose odd s, odd_add_of_even_of_odd `even (2^(succ n))` this),
have aux₂ : odd s ↔ 0 ∈ insert (succ n) (of_nat s), from iff.intro
assert aux₂ : odd s ↔ 0 ∈ insert (succ n) (of_nat s), from iff.intro
(suppose odd s, finset.mem_insert_of_mem _ (iff.mpr !odd_of_zero_mem this))
(suppose 0 ∈ insert (succ n) (of_nat s), or.elim (eq_or_mem_of_mem_insert this)
(by contradiction)
(suppose 0 ∈ of_nat s, iff.mp !odd_of_zero_mem this)),
calc
0 ∈ of_nat (2^(succ n) + s) ↔ odd (2^(succ n) + s) : odd_of_zero_mem
... ↔ odd s : aux₁
... ↔ 0 ∈ insert (succ n) (of_nat s) : aux₂
0 ∈ of_nat (2^(succ n) + s) ↔ odd (2^(succ n) + s) : by apply odd_of_zero_mem
... ↔ odd s : by exact aux₁
... ↔ 0 ∈ insert (succ n) (of_nat s) : by exact aux₂
| (succ m) :=
assert aux : m ∈ insert n (of_nat (s div 2)) ↔ succ m ∈ insert (succ n) (of_nat s), from iff.intro
(assume hl, or.elim (eq_or_mem_of_mem_insert hl)
@ -173,10 +173,10 @@ private lemma of_nat_eq_insert : ∀ {n s : nat}, n ∉ of_nat s → of_nat (2^n
(suppose succ m ∈ of_nat s, finset.mem_insert_of_mem _ (iff.mp !succ_mem_of_nat this))),
calc
succ m ∈ of_nat (2^(succ n) + s) ↔ succ m ∈ of_nat (2^n * 2 + s) : by rewrite pow_succ'
... ↔ m ∈ of_nat ((2^n * 2 + s) div 2) : succ_mem_of_nat
... ↔ m ∈ of_nat ((2^n * 2 + s) div 2) : by apply succ_mem_of_nat
... ↔ m ∈ of_nat (2^n + s div 2) : by rewrite [add.comm, add_mul_div_self (dec_trivial : 2 > 0), add.comm]
... ↔ m ∈ insert n (of_nat (s div 2)) : by rewrite ih
... ↔ succ m ∈ insert (succ n) (of_nat s) : aux,
... ↔ succ m ∈ insert (succ n) (of_nat s) : by exact aux,
gen x)
lemma of_nat_to_nat (s : finset nat) : of_nat (to_nat s) = s :=