Search for blocks/addresses/...

Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply set_ext with setminus (binintersect x0 x1) x2, binintersect x0 (setminus x1 x2) leaving 2 subgoals.
Let x3 of type ι be given.
Assume H0: x3 ∈ setminus (binintersect x0 x1) x2.
Apply setminusE with binintersect x0 x1, x2, x3, x3 ∈ binintersect x0 (setminus x1 x2) leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1: x3 ∈ binintersect x0 x1.
Assume H2: nIn x3 x2.
Apply binintersectE with x0, x1, x3, x3 ∈ binintersect x0 (setminus x1 x2) leaving 2 subgoals.
The subproof is completed by applying H1.
Assume H3: x3 ∈ x0.
Assume H4: x3 ∈ x1.
Apply binintersectI with x0, setminus x1 x2, x3 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply setminusI with x1, x2, x3 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H2.
Let x3 of type ι be given.
Assume H0: x3 ∈ binintersect x0 (setminus x1 x2).
Apply binintersectE with x0, setminus x1 x2, x3, x3 ∈ setminus (binintersect x0 x1) x2 leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1: x3 ∈ x0.
Assume H2: x3 ∈ setminus x1 x2.
Apply setminusE with x1, x2, x3, x3 ∈ setminus (binintersect x0 x1) x2 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3: x3 ∈ x1.
Assume H4: nIn x3 x2.
Apply setminusI with binintersect x0 x1, x2, x3 leaving 2 subgoals.
Apply binintersectI with x0, x1, x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
■