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move tiago's lemma to Nat lib

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This commit is contained in:
Rígille S. B. Menezes 2021-12-03 14:05:14 -03:00
parent 5f7e58366e
commit 28e6ab48bc
3 changed files with 21 additions and 18 deletions
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19
base/Nat/ltn/sub_right.kind Normal file
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@ -0,0 +1,19 @@
Nat.ltn.sub_right(
x: Nat, y: Nat, z: Nat
H: Equal(Bool, Nat.ltn(y, Nat.sub(z, x)), true)
): Equal(Bool, Nat.lte(Nat.add(x y), z), true)
case x with H {
succ:
case z with H {
succ:
let H = H :: rewrite X in Nat.lte(Nat.succ(y), X) == Bool.true with (Nat.sub.succ_both(z.pred,x.pred))
let rec = Nat.ltn.sub_right(x.pred, y, z.pred, H)
rec
zero:
let H = H :: Nat.lte(Nat.succ(y),0) == Bool.true
Empty.absurd!(Bool.false_neq_true(H))
}!
zero:
let H = H :: Nat.lte(Nat.succ(y), z) == Bool.true
Nat.lte.succ_left!!(H)
}!

4
base/RLP/aux.kind
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@ -5,7 +5,7 @@ RLP.aux.split.0(
H: Equal<Bool>(Nat.lte(List.length!(payload), 55), true)
): Pair.new(Bytes, Bytes, payload, tail) == RLP.split.length(128, Nat.to_u8(Nat.add(128, List.length!(payload))) & payload ++ tail)
let chain = Nat.Order.chain(List.length(U8,payload), 55, 126, H, refl)
let H0 = RLP.new_aux.Nat.lte.max_add(128, List.length(U8,payload), 255, chain)
let H0 = Nat.ltn.sub_right(128, List.length(U8,payload), 255, chain)
let H1 = Nat.to_u8.safe_conversion(Nat.add(128,List.length(U8,payload)), H0)
replace X with H1 in Pair.new(Bytes,Bytes,payload,tail) == Nat.lte(Nat.sub(X,128),55,() Pair(Bytes,Bytes),Bytes.split(List.concat(U8,payload,tail),Nat.sub(U8.to_nat(Nat.to_u8(Nat.add(128,List.length(U8,payload)))),128)),Bytes.split(List.concat(U8,payload,tail),Nat.sub(Nat.sub(U8.to_nat(Nat.to_u8(Nat.add(128,List.length(U8,payload)))),128),56),() Pair(Bytes,Bytes),(length) (tail) Bytes.split(tail,Bytes.to_nat(length))))
let H2 = Nat.sub.add.left(128, List.length(U8,payload)) :: rewrite X in Nat.sub(X,128) == List.length(U8,payload) with Nat.add.comm(List.length(U8,payload),128)
@ -52,7 +52,7 @@ RLP.aux.split.2(
H: Equal<Bool>(Nat.lte(List.length!(payload), 55), true)
): Pair.new(Bytes, Bytes, payload, tail) == RLP.split.length(192, Nat.to_u8(Nat.add(192, List.length!(payload))) & payload ++ tail)
let chain = Nat.Order.chain(List.length(U8,payload), 55, 62, H, refl)
let H0 = RLP.new_aux.Nat.lte.max_add(192, List.length(U8,payload), 255, chain)
let H0 = Nat.ltn.sub_right(192, List.length(U8,payload), 255, chain)
let H1 = Nat.to_u8.safe_conversion(Nat.add(192,List.length(U8,payload)), H0)
replace X with H1 in Pair.new(Bytes,Bytes,payload,tail) == Nat.lte(Nat.sub(X,192),55,() Pair(Bytes,Bytes),Bytes.split(List.concat(U8,payload,tail),Nat.sub(X,192)),Bytes.split(List.concat(U8,payload,tail),Nat.sub(Nat.sub(X,192),56),() Pair(Bytes,Bytes),(length) (tail) Bytes.split(tail,Bytes.to_nat(length))))
let H2 = Nat.sub.add.left(192, List.length(U8,payload)) :: rewrite X in Nat.sub(X,192) == List.length(U8,payload) with Nat.add.comm(List.length(U8,payload),192)

16
base/RLP/new_aux.kind
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@ -1,16 +0,0 @@
RLP.new_aux.Nat.lte.max_add(x : Nat, y : Nat, z : Nat, H : Nat.lte(Nat.succ(y), z - x) == true)
: Nat.lte(Nat.add(x y), z) == true
case x with H {
succ : case z with H {
succ :
let H = H :: rewrite X in Nat.lte(Nat.succ(y), X) == Bool.true with (Nat.sub.succ_both(z.pred,x.pred))
let rec = RLP.new_aux.Nat.lte.max_add(x.pred, y, z.pred, H)
rec
zero :
let H = H :: Nat.lte(Nat.succ(y),0) == Bool.true
Empty.absurd!(Bool.false_neq_true(H))
}!
zero :
let H = H :: Nat.lte(Nat.succ(y), z) == Bool.true
Nat.lte.succ_left!!(H)
}!