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Rename some confusing fields (#51)

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Patrick Stevens
2019-10-13 09:31:54 +01:00
committed by GitHub
parent 96d15c6017
commit 959071214e
21 changed files with 441 additions and 441 deletions
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14
LectureNotes/NumbersAndSets/Lecture1.agda
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@@ -9,9 +9,9 @@ open import Numbers.Naturals.Exponentiation
open import Numbers.Primes.PrimeNumbers
open import Maybe
open import Semirings.Definition
open import Semirings.Solver
import Semirings.Solver
module NatSolver = Semirings.Solver ℕSemiring multiplicationNIsCommutative
open module NatSolver = Semirings.Solver ℕSemiring multiplicationNIsCommutative
module LectureNotes.NumbersAndSets.Lecture1 where
@@ -43,13 +43,13 @@ n3Bigger' zero = inr refl
n3Bigger' (succ n) with n3Bigger (succ n)
n3Bigger' (succ n) | inr f = f
_!!N_ = NatSolver._!!_
-- How to use the semiring solver
-- The process is very mechanical; I haven't yet worked out how to do reflection,
-- so there's quite a bit of transcribing expressions into the Expr form.
-- The first two arguments to !!N are totally mindless in construction.
-- The first two arguments to from-to-by are totally mindless in construction.
proof : (n : ℕ) → ((n *N n) +N ((2 *N n) +N 1)) ≡ (n +N 1) *N (n +N 1)
proof n =
(plus (times (const n) (const n)) (plus (times (succ (succ zero)) (const n)) (succ zero)) !!N times (plus (const n) (succ zero)) (plus (const n) (succ zero)))
(applyEquality (λ i → succ (n *N n) +N (n +N i)) ((const n !!N plus (const n) zero) refl))
from plus (times (const n) (const n)) (plus (times (succ (succ zero)) (const n)) (succ zero))
to times (plus (const n) (succ zero)) (plus (const n) (succ zero))
by
applyEquality (λ i → succ (n *N n) +N (n +N i)) ((from (const n) to (plus (const n) zero) by refl))