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_Ring_with_id_E with x0, x1, x2, x3, x4, ∀ x5 . x5x0explicit_Ring_minus x0 x1 x3 x4 x5 = x4 (explicit_Ring_minus x0 x1 x3 x4 x2) x5.
Assume H0: explicit_Ring_with_id x0 x1 x2 x3 x4.
Assume H1: ∀ x5 . x5x0∀ x6 . x6x0x3 x5 x6x0.
Assume H2: ∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0x3 x5 (x3 x6 x7) = x3 (x3 x5 x6) x7.
Assume H3: ∀ x5 . x5x0∀ x6 . x6x0x3 x5 x6 = x3 x6 x5.
Assume H4: x1x0.
Assume H5: ∀ x5 . x5x0x3 x1 x5 = x5.
Assume H6: ∀ x5 . x5x0∃ x6 . and (x6x0) (x3 x5 x6 = x1).
Assume H7: ∀ x5 . x5x0∀ x6 . x6x0x4 x5 x6x0.
Assume H8: ∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0x4 x5 (x4 x6 x7) = x4 (x4 x5 x6) x7.
Assume H9: x2x0.
Assume H10: x2 = x1∀ x5 : ο . x5.
Assume H11: ∀ x5 . x5x0x4 x2 x5 = x5.
Assume H12: ∀ x5 . x5x0x4 x5 x2 = x5.
Assume H13: ∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0x4 x5 (x3 x6 x7) = x3 (x4 x5 x6) (x4 x5 x7).
Assume H14: ∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0x4 (x3 x5 x6) x7 = x3 (x4 x5 x7) (x4 x6 x7).
Let x5 of type ι be given.
Assume H15: x5x0.
Claim L16: ...
...
Claim L17: ...
...
Apply explicit_Ring_with_id_plus_cancelL with x0, x1, x2, x3, x4, x5, explicit_Ring_minus x0 x1 x3 x4 x5, x4 (explicit_Ring_minus x0 x1 x3 x4 x2) x5 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H15.
The subproof is completed by applying L16.
The subproof is completed by applying L17.
Apply explicit_Ring_with_id_minus_R with x0, x1, x2, x3, x4, x5, λ x6 x7 . x7 = x3 x5 (x4 (explicit_Ring_minus x0 x1 x3 x4 x2) x5) leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H15.
Let x6 of type ιιο be given.
Apply H11 with x5, λ x7 x8 . x3 x7 ... = ..., ... leaving 2 subgoals.
...
...