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.
Let x4 of type ι be given.
Assume H0: x0 = x1 ⟶ ∀ x5 : ο . x5.
Assume H1: x0 = x2 ⟶ ∀ x5 : ο . x5.
Assume H2: x0 = x3 ⟶ ∀ x5 : ο . x5.
Assume H3: x0 = x4 ⟶ ∀ x5 : ο . x5.
Assume H4: x1 = x2 ⟶ ∀ x5 : ο . x5.
Assume H5: x1 = x3 ⟶ ∀ x5 : ο . x5.
Assume H6: x1 = x4 ⟶ ∀ x5 : ο . x5.
Assume H7: x2 = x3 ⟶ ∀ x5 : ο . x5.
Assume H8: x2 = x4 ⟶ ∀ x5 : ο . x5.
Assume H9: x3 = x4 ⟶ ∀ x5 : ο . x5.
Apply equip_sym with
u5,
SetAdjoin (SetAdjoin (SetAdjoin (UPair x0 x1) x2) x3) x4.
Apply unknownprop_eab190d6552dbda6c7d00c3e93c1ad9385698a8d73462a2a4e5795b67701610d with
u4,
SetAdjoin (SetAdjoin (UPair x0 x1) x2) x3,
x4 leaving 2 subgoals.
Claim L11:
or (or (or (x4 = x0) (x4 = x1)) (x4 = x2)) (x4 = x3)Apply unknownprop_3de4fed6100f7a1644d3bcc671dd5818f525687e19a89aa1d64708dea3801718 with
x0,
x1,
x2,
x3,
x4,
λ x5 . or (or (or (x5 = x0) (x5 = x1)) (x5 = x2)) (x5 = x3) leaving 5 subgoals.
The subproof is completed by applying H10.
Apply orIL with
or (or (x0 = x0) (x0 = x1)) (x0 = x2),
x0 = x3.
Apply orIL with
or (x0 = x0) (x0 = x1),
x0 = x2.
Apply orIL with
x0 = x0,
x0 = x1.
Let x5 of type ι → ι → ο be given.
Assume H11: x5 x0 x0.
The subproof is completed by applying H11.
Apply orIL with
or (or (x1 = x0) (x1 = x1)) (x1 = x2),
x1 = x3.
Apply orIL with
or (x1 = x0) (x1 = x1),
x1 = x2.
Apply orIR with
x1 = x0,
x1 = x1.
Let x5 of type ι → ι → ο be given.
Assume H11: x5 x1 x1.
The subproof is completed by applying H11.
Apply orIL with
or (or (x2 = x0) (x2 = x1)) (x2 = x2),
x2 = x3.
Apply orIR with
or (x2 = x0) (x2 = x1),
x2 = x2.
Let x5 of type ι → ι → ο be given.
Assume H11: x5 x2 x2.
The subproof is completed by applying H11.
Apply L11 with
False leaving 2 subgoals.
Assume H12:
or (or (x4 = x0) (x4 = x1)) (x4 = x2).
Apply H12 with
False leaving 2 subgoals.
Assume H13:
or (x4 = x0) (x4 = x1).
Apply H13 with
False leaving 2 subgoals.
Assume H14: x4 = x0.
Apply H3.
Let x5 of type ι → ι → ο be given.
The subproof is completed by applying H14 with λ x6 x7 . x5 x7 x6.
Assume H14: x4 = x1.
Apply H6.
Let x5 of type ι → ι → ο be given.
The subproof is completed by applying H14 with λ x6 x7 . x5 x7 x6.
Assume H13: x4 = x2.
Apply H8.
Let x5 of type ι → ι → ο be given.
The subproof is completed by applying H13 with λ x6 x7 . x5 x7 x6.
Assume H12: x4 = x3.
Apply H9.
Let x5 of type ι → ι → ο be given.
The subproof is completed by applying H12 with λ x6 x7 . x5 x7 x6.