Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H0: x0 = x1 ⟶ ∀ x4 : ο . x4.
Assume H1: x0 = x2 ⟶ ∀ x4 : ο . x4.
Assume H2: x0 = x3 ⟶ ∀ x4 : ο . x4.
Assume H3: x1 = x2 ⟶ ∀ x4 : ο . x4.
Assume H4: x1 = x3 ⟶ ∀ x4 : ο . x4.
Assume H5: x2 = x3 ⟶ ∀ x4 : ο . x4.
Apply equip_sym with
u4,
SetAdjoin (SetAdjoin (UPair x0 x1) x2) x3.
Apply unknownprop_eab190d6552dbda6c7d00c3e93c1ad9385698a8d73462a2a4e5795b67701610d with
u3,
SetAdjoin (UPair x0 x1) x2,
x3 leaving 2 subgoals.
Claim L7:
or (or (x3 = x0) (x3 = x1)) (x3 = x2)Apply unknownprop_81da4a4b6c1b1603a521d080942fe6e652095cdddea7d0d491d4c44dcea723fa with
x0,
x1,
x2,
x3,
λ x4 . or (or (x4 = x0) (x4 = x1)) (x4 = x2) leaving 4 subgoals.
The subproof is completed by applying H6.
Apply orIL with
or (x0 = x0) (x0 = x1),
x0 = x2.
Apply orIL with
x0 = x0,
x0 = x1.
Let x4 of type ι → ι → ο be given.
Assume H7: x4 x0 x0.
The subproof is completed by applying H7.
Apply orIL with
or (x1 = x0) (x1 = x1),
x1 = x2.
Apply orIR with
x1 = x0,
x1 = x1.
Let x4 of type ι → ι → ο be given.
Assume H7: x4 x1 x1.
The subproof is completed by applying H7.
Apply orIR with
or (x2 = x0) (x2 = x1),
x2 = x2.
Let x4 of type ι → ι → ο be given.
Assume H7: x4 x2 x2.
The subproof is completed by applying H7.
Apply L7 with
False leaving 2 subgoals.
Assume H8:
or (x3 = x0) (x3 = x1).
Apply H8 with
False leaving 2 subgoals.
Assume H9: x3 = x0.
Apply H2.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H9 with λ x5 x6 . x4 x6 x5.
Assume H9: x3 = x1.
Apply H4.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H9 with λ x5 x6 . x4 x6 x5.
Assume H8: x3 = x2.
Apply H5.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H8 with λ x5 x6 . x4 x6 x5.
Apply equip_sym with
SetAdjoin (UPair x0 x1) x2,
u3.
Apply unknownprop_01a9c78d2ff9508973a3397619af294eba02d9395696c331bc156cf4e0508f7d with
x0,
x1,
x2 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H3.