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.
Let x3 of type ιιι be given.
Let x4 of type ιιι be given.
Apply explicit_Field_E with x0, x1, x2, x3, x4, ∀ x5 . prim1 x5 x0x4 (explicit_Field_minus x0 x1 x2 x3 x4 x5) (explicit_Field_minus x0 x1 x2 x3 x4 x5) = x4 x5 x5.
Assume H0: explicit_Field x0 x1 x2 x3 x4.
Assume H1: ∀ x5 . prim1 x5 x0∀ x6 . prim1 x6 x0prim1 (x3 x5 x6) x0.
Assume H2: ∀ x5 . prim1 x5 x0∀ x6 . prim1 x6 x0∀ x7 . prim1 x7 x0x3 x5 (x3 x6 x7) = x3 (x3 x5 x6) x7.
Assume H3: ∀ x5 . prim1 x5 x0∀ x6 . prim1 x6 x0x3 x5 x6 = x3 x6 x5.
Assume H4: prim1 x1 x0.
Assume H5: ∀ x5 . prim1 x5 x0x3 x1 x5 = x5.
Assume H6: ∀ x5 . prim1 x5 x0∃ x6 . and (prim1 x6 x0) (x3 x5 x6 = x1).
Assume H7: ∀ x5 . prim1 x5 x0∀ x6 . prim1 x6 x0prim1 (x4 x5 x6) x0.
Assume H8: ∀ x5 . prim1 x5 x0∀ x6 . prim1 x6 x0∀ x7 . prim1 x7 x0x4 x5 (x4 x6 x7) = x4 (x4 x5 x6) x7.
Assume H9: ∀ x5 . prim1 x5 x0∀ x6 . prim1 x6 x0x4 x5 x6 = x4 x6 x5.
Assume H10: prim1 x2 x0.
Assume H11: x2 = x1∀ x5 : ο . x5.
Assume H12: ∀ x5 . prim1 x5 x0x4 x2 x5 = x5.
Assume H13: ∀ x5 . prim1 x5 x0(x5 = x1∀ x6 : ο . x6)∃ x6 . and (prim1 x6 x0) (x4 x5 x6 = x2).
Assume H14: ∀ x5 . prim1 x5 x0∀ x6 . prim1 x6 x0∀ x7 . prim1 x7 x0x4 x5 (x3 x6 x7) = x3 (x4 x5 x6) (x4 x5 x7).
Let x5 of type ι be given.
Assume H15: prim1 x5 x0.
Apply explicit_Field_minus_mult with x0, x1, x2, x3, x4, x5, λ x6 x7 . x4 x7 x7 = x4 x5 x5 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H15.
Claim L16: ...
...
Claim L17: ...
...
Apply H8 with explicit_Field_minus x0 x1 x2 x3 x4 x2, x5, x4 (explicit_Field_minus x0 ... ... ... ... ...) ..., ... leaving 4 subgoals.
...
...
...
...