Theorem: ℤω.natNorm_coe (Mordell4/Eisenstein.lean)

State before:
a b c : ℤω
⊢ ↑normSq (OneHom.toFun (↑↑inclusion) a) = ↑(natNorm a)
Tactic:
unfold natNorm
State after:
a b c : ℤω
⊢ ↑normSq (OneHom.toFun (↑↑inclusion) a) = ↑(natAbs (norm a))

State before:
a b c : ℤω
⊢ ↑normSq (OneHom.toFun (↑↑inclusion) a) = ↑(natAbs (norm a))
Tactic:
rw [normSq_coe]
State after:
a b c : ℤω
⊢ ↑(norm a) = ↑(natAbs (norm a))

State before:
a b c : ℤω
⊢ ↑(norm a) = ↑(natAbs (norm a))
Tactic:
suffices : a.norm = a.norm.natAbs
State after:
a b c : ℤω
this : norm a = ↑(natAbs (norm a))
⊢ ↑(norm a) = ↑(natAbs (norm a))

case this
a b c : ℤω
⊢ norm a = ↑(natAbs (norm a))

State before:
a b c : ℤω
this : norm a = ↑(natAbs (norm a))
⊢ ↑(norm a) = ↑(natAbs (norm a))

case this
a b c : ℤω
⊢ norm a = ↑(natAbs (norm a))
Tactic:
congr
State after:
case this
a b c : ℤω
⊢ norm a = ↑(natAbs (norm a))

State before:
case this
a b c : ℤω
⊢ norm a = ↑(natAbs (norm a))
Tactic:
exact this
State after:
no goals