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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 → ι → ι be given.
Let x5 of type ι → ι → ι be given.
Let x6 of type ι → ο be given.
Let x7 of type ι → ο be given.
Let x8 of type ι → ο be given.
Let x9 of type ι → ο be given.
Apply and5I with x0 = x1, ∀ x10 : ι → ο . (∀ x11 . x10 x11 ⟶ prim1 x11 x0) ⟶ x2 x10 = x3 x10, ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x4 x10 x11 = x5 x10 x11, ∀ x10 . prim1 x10 x0 ⟶ x6 x10 = x7 x10, ∀ x10 . prim1 x10 x0 ⟶ x8 x10 = x9 x10 leaving 5 subgoals.
The subproof is completed by applying L2.
Let x10 of type ι → ο be given.
Assume H3: ∀ x11 . x10 x11 ⟶ prim1 x11 x0. Apply unknownprop_b8b08deb4ce9fe08026cdd946e072c126ec647e59db3da144b4ba7b8a3ae34db with x0, x2, x4, x6, x8, x10, λ x11 x12 : ο . x12 = x3 x10 leaving 2 subgoals.
The subproof is completed by applying H3.
Claim L4: ∀ x11 . x10 x11 ⟶ prim1 x11 x1Apply L2 with λ x11 x12 . ∀ x13 . x10 x13 ⟶ prim1 x13 x11.
The subproof is completed by applying H3.
Apply H0 with λ x11 x12 . decode_c (f482f.. x12 (4ae4a.. 4a7ef..)) x10 = x3 x10.
Let x11 of type ο → ο → ο be given.
Apply unknownprop_b8b08deb4ce9fe08026cdd946e072c126ec647e59db3da144b4ba7b8a3ae34db with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.
The subproof is completed by applying L4.
Let x10 of type ι be given.
Let x11 of type ι be given.
Apply unknownprop_361f56d0f0f7721253f46e481bb5360cdc5ca15df56553eab122c1c7545a0139 with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 . x13 = x5 x10 x11 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply L2 with λ x12 x13 . prim1 x10 x12.
The subproof is completed by applying H3.
Apply L2 with λ x12 x13 . prim1 x11 x12.
The subproof is completed by applying H4.
Apply H0 with λ x12 x13 . e3162.. (f482f.. x13 (4ae4a.. (4ae4a.. 4a7ef..))) x10 x11 = x5 x10 x11.
Let x12 of type ι → ι → ο be given.
Apply unknownprop_361f56d0f0f7721253f46e481bb5360cdc5ca15df56553eab122c1c7545a0139 with x1, x3, x5, x7, x9, x10, x11, λ x13 x14 . x12 x14 x13 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x10 of type ι be given.
Apply unknownprop_ed9d8ed93a3bd6bbea7e5eef5e37a69bd0d4a2b9d800738495ab1d6c9090ce53 with x0, x2, x4, x6, x8, x10, λ x11 x12 : ο . x12 = x7 x10 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with λ x11 x12 . prim1 x10 x11.
The subproof is completed by applying H3.
Apply H0 with λ x11 x12 . decode_p (f482f.. x12 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x10 = x7 x10.
Let x11 of type ο → ο → ο be given.
Apply unknownprop_ed9d8ed93a3bd6bbea7e5eef5e37a69bd0d4a2b9d800738495ab1d6c9090ce53 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.
The subproof is completed by applying L4.
Let x10 of type ι be given.
Apply unknownprop_c34a240ffb36057c4f0b75b4a6d2ec4faae5845aa6182897b19bb5dea423b792 with x0, x2, x4, x6, x8, x10, λ x11 x12 : ο . x12 = x9 x10 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with λ x11 x12 . prim1 x10 ....
Apply H0 with λ x11 x12 . decode_p (f482f.. x12 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x10 = x9 x10.
Let x11 of type ο → ο → ο be given.
Apply unknownprop_c34a240ffb36057c4f0b75b4a6d2ec4faae5845aa6182897b19bb5dea423b792 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.
The subproof is completed by applying L4.
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