| pf |
|---|
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 be given.
Let x5 of type ι → ι be given.
Let x6 of type ι → ι → ο be given.
Let x7 of type ι → 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 ⟶ x4 x10 = x5 x10, ∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 x10 x11 = x7 x10 x11, ∀ 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_76e354ddaaf5ea9ad81b81b42ecb99d89d4b1fa6ed8985ecdc96882fad13e5e2 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_76e354ddaaf5ea9ad81b81b42ecb99d89d4b1fa6ed8985ecdc96882fad13e5e2 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_4fc332daa2b99c12352c1d15dd590601e19fa9821e6ba1b89579fa710ea0d2a1 with x0, x2, x4, x6, x8, x10, λ x11 x12 . x12 = x5 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 . f482f.. (f482f.. x12 (4ae4a.. (4ae4a.. 4a7ef..))) x10 = x5 x10.
Let x11 of type ι → ι → ο be given.
Apply unknownprop_4fc332daa2b99c12352c1d15dd590601e19fa9821e6ba1b89579fa710ea0d2a1 with x1, x3, x5, x7, x9, x10, λ x12 x13 . 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_d1c17917281d83596bb85722df08e758bcfafa86d8f4cbeab8958beeb91edd03 with x0, x2, x4, x6, x8, x10, x11, λ x12 x13 : ο . x13 = x7 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 . 2b2e3.. (f482f.. x13 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x10 x11 = x7 x10 x11.
Let x12 of type ο → ο → ο be given.
Apply unknownprop_d1c17917281d83596bb85722df08e758bcfafa86d8f4cbeab8958beeb91edd03 with x1, x3, x5, x7, x9, x10, x11, λ x13 x14 : ο . 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_3ae4f9831850519ac9905885268b7578d3c76b0ebb4555db0b7a62ea1e85c525 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_3ae4f9831850519ac9905885268b7578d3c76b0ebb4555db0b7a62ea1e85c525 with x1, x3, x5, x7, x9, x10, λ x12 x13 : ο . x11 x13 x12.
The subproof is completed by applying L4.
■ |
|