Claim L0:
∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ∈ x0) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ x1 x3 x4 = x2 x3 x4) ⟶ 28b0a.. x0 x2 = 28b0a.. x0 x1The subproof is completed by applying unknownprop_9e7ec4148d62bafcd9e146d1756f4a7aed7c3eb8fc00334b6fe1712064d0a901.
Claim L1:
∀ x0 : ι → ι → ι . (∀ x1 . x1 ∈ 1 ⟶ ∀ x2 . x2 ∈ 1 ⟶ 0 = x0 x1 x2) ⟶ 28b0a.. 1 x0Let x0 of type ι → ι → ι be given.
Assume H1: ∀ x1 . x1 ∈ 1 ⟶ ∀ x2 . x2 ∈ 1 ⟶ 0 = x0 x1 x2.
Let x1 of type ι be given.
Assume H2: x1 ∈ 1.
Let x2 of type ι be given.
Assume H3: x2 ∈ 1.
Let x3 of type ι be given.
Assume H4: x3 ∈ 1.
Apply H1 with
x1,
x2,
λ x4 x5 . x0 x4 x3 = x0 x1 (x0 x2 x3) leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply H1 with
x2,
x3,
λ x4 x5 . x0 0 x3 = x0 x1 x4 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply H1 with
0,
x3,
λ x4 x5 . x4 = x0 x1 0 leaving 3 subgoals.
The subproof is completed by applying In_0_1.
The subproof is completed by applying H4.
Apply H1 with
x1,
0 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying In_0_1.
Apply unknownprop_6482bf17c7629de0c611c16b71ae30c036294b46cbc3e9f673f7271f20ce0d70 with
28b0a.. leaving 2 subgoals.
The subproof is completed by applying L0.
The subproof is completed by applying L1.