Search for blocks/addresses/...

Proofgold Proof

pf
Let x0 of type ι(ιιο) → (ιιο) → (ιο) → ο be given.
Let x1 of type ι be given.
Let x2 of type ιιο be given.
Let x3 of type ιιο be given.
Let x4 of type ιο be given.
Assume H0: ∀ x5 : ι → ι → ο . (∀ x6 . x6x1∀ x7 . x7x1iff (x2 x6 x7) (x5 x6 x7))∀ x6 : ι → ι → ο . (∀ x7 . x7x1∀ x8 . x8x1iff (x3 x7 x8) (x6 x7 x8))∀ x7 : ι → ο . (∀ x8 . x8x1iff (x4 x8) (x7 x8))x0 x1 x5 x6 x7 = x0 x1 x2 x3 x4.
Apply pack_r_r_p_0_eq2 with x1, x2, x3, x4, λ x5 x6 . x0 x5 (decode_r (ap (pack_r_r_p x1 x2 x3 x4) 1)) (decode_r (ap (pack_r_r_p x1 x2 x3 x4) 2)) (decode_p (ap (pack_r_r_p x1 x2 x3 x4) 3)) = x0 x1 x2 x3 x4.
Apply H0 with decode_r (ap (pack_r_r_p x1 x2 x3 x4) 1), decode_r (ap (pack_r_r_p x1 x2 x3 x4) 2), decode_p (ap (pack_r_r_p x1 x2 x3 x4) 3) leaving 3 subgoals.
Let x5 of type ι be given.
Assume H1: x5x1.
Let x6 of type ι be given.
Assume H2: x6x1.
Apply pack_r_r_p_1_eq2 with x1, x2, x3, x4, x5, x6, λ x7 x8 : ο . iff (x2 x5 x6) x7 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x2 x5 x6.
Let x5 of type ι be given.
Assume H1: x5x1.
Let x6 of type ι be given.
Assume H2: x6x1.
Apply pack_r_r_p_2_eq2 with x1, x2, x3, x4, x5, x6, λ x7 x8 : ο . iff (x3 x5 x6) x7 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x3 x5 x6.
Let x5 of type ι be given.
Assume H1: x5x1.
Apply pack_r_r_p_3_eq2 with x1, x2, x3, x4, x5, λ x6 x7 : ο . iff (x4 x5) x6 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x4 x5.