Search for blocks/addresses/...

Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: RealsStruct x0.
Let x1 of type ι be given.
Assume H1: x1 ∈ field0 x0.
Claim L2: Field_minus (Field_of_RealsStruct x0) x1 ∈ field0 x0
Apply RealsStruct_minus_clos with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Claim L3: Field_minus (Field_of_RealsStruct x0) (Field_minus (Field_of_RealsStruct x0) x1) ∈ field0 x0
Apply RealsStruct_minus_clos with x0, Field_minus (Field_of_RealsStruct x0) x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L2.
Apply RealsStruct_plus_cancelL with x0, Field_minus (Field_of_RealsStruct x0) x1, Field_minus (Field_of_RealsStruct x0) (Field_minus (Field_of_RealsStruct x0) x1), x1 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L2.
The subproof is completed by applying L3.
The subproof is completed by applying H1.
Apply RealsStruct_minus_L with x0, x1, λ x2 x3 . field1b x0 (Field_minus (Field_of_RealsStruct x0) x1) (Field_minus (Field_of_RealsStruct x0) (Field_minus (Field_of_RealsStruct x0) x1)) = x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply RealsStruct_minus_R with x0, Field_minus (Field_of_RealsStruct x0) x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L2.
■