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Add new theorems and proofs #22

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14 changes: 2 additions & 12 deletions EasyLean/Basic.lean
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import Mathlib.Data.Real.Basic
import Mathlib.Tactic.Linarith

theorem mathd_algebra_513
(a b : ℝ)
(h₀ : 3 * a + 2 * b = 5)
(h₁ : a + b = 2) :
a = 1 ∧ b = 1 := by
sorry

theorem eq_four : ∀ a b c d : Nat, a = b → a = d → a = c → c = b := by
sorry
import EasyLean.Theorems.MathdAlgebra513
import EasyLean.Theorems.EqFour
5 changes: 5 additions & 0 deletions EasyLean/Theorems/EqFour.lean
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import Mathlib

theorem eq_four (a b c d : Nat) : a = b → a = d → a = c → c = b := by
intro h0 h1 h2
simpa using Eq.trans h2.symm h0
9 changes: 9 additions & 0 deletions EasyLean/Theorems/MathdAlgebra513.lean
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import Mathlib

theorem mathd_algebra_513
(a b : Real) (h0 : 3 * a + 2 * b = 5) (h1 : a + b = 2) : a = 1 ∧ b = 1 := by
have ha : a = 1 := by
linear_combination h0 - (2 : ℚ) * h1
have hb : b = 1 := by
linarith [h1, ha]
exact ⟨ha, hb⟩