Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type (ι → ο) → ο be given.
Let x3 of type (ι → ο) → ο be given.
Let x4 of type ι → ο be given.
Let x5 of type ι → ο be given.
Apply unknownprop_ef3967aea30eb796b077b0115556310bcc08bf63575294f0ec1a3f67adc468c7 with
01d88.. x0 x2 x4,
x1,
x3,
x5.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x6 x7 . x0 = x7.
The subproof is completed by applying unknownprop_6d2dce7078e61066802501dd67fa0f8d1d04bdbc9f24e77dcf05cf9a71e757b2 with x0, x2, x4.
Apply and3I with
x0 = x1,
∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x0) ⟶ x2 x6 = x3 x6,
∀ x6 . prim1 x6 x0 ⟶ x4 x6 = x5 x6 leaving 3 subgoals.
The subproof is completed by applying L2.
Let x6 of type ι → ο be given.
Assume H3:
∀ x7 . x6 x7 ⟶ prim1 x7 x0.
Apply unknownprop_ed29eb2a3dee7023c289bdb42a804e4893144f032afd50419f3fc25fc78c2df2 with
x0,
x2,
x4,
x6,
λ x7 x8 : ο . x8 = x3 x6 leaving 2 subgoals.
The subproof is completed by applying H3.
Claim L4:
∀ x7 . x6 x7 ⟶ prim1 x7 x1Apply L2 with
λ x7 x8 . ∀ x9 . x6 x9 ⟶ prim1 x9 x7.
The subproof is completed by applying H3.
Apply H0 with
λ x7 x8 . decode_c (f482f.. x8 (4ae4a.. 4a7ef..)) x6 = x3 x6.
Let x7 of type ο → ο → ο be given.
Apply unknownprop_ed29eb2a3dee7023c289bdb42a804e4893144f032afd50419f3fc25fc78c2df2 with
x1,
x3,
x5,
x6,
λ x8 x9 : ο . x7 x9 x8.
The subproof is completed by applying L4.
Let x6 of type ι be given.
Apply unknownprop_b158b7086827b8c679d5ced1a07e0e8b2c2264c4046da20f1d53c64aab107031 with
x0,
x2,
x4,
x6,
λ x7 x8 : ο . x8 = x5 x6 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with
λ x7 x8 . prim1 x6 x7.
The subproof is completed by applying H3.
Apply H0 with
λ x7 x8 . decode_p (f482f.. x8 (4ae4a.. (4ae4a.. 4a7ef..))) x6 = x5 x6.
Let x7 of type ο → ο → ο be given.
Apply unknownprop_b158b7086827b8c679d5ced1a07e0e8b2c2264c4046da20f1d53c64aab107031 with
x1,
x3,
x5,
x6,
λ x8 x9 : ο . x7 x9 x8.
The subproof is completed by applying L4.