Exact expanded PA statement
forall b c z d a l. (forall ff_i_transport_l. (exists ff_lt_transport_l_bound. ff_lt_transport_l_bound + S ff_i_transport_l = l) -> (((exists ff_h_transport_l_decoded. ff_h_transport_l_decoded + S (a + ff_i_transport_l) = S ((S (ff_i_transport_l)) * c)) /\ exists ff_q_transport_l_decoded. b = ff_q_transport_l_decoded * S ((S (ff_i_transport_l)) * c) + (a + ff_i_transport_l)))) -> (forall ff_i_transport_r. (exists ff_lt_transport_r_bound. ff_lt_transport_r_bound + S ff_i_transport_r = l) -> (((exists ff_h_transport_r_decoded. ff_h_transport_r_decoded + S (a + ff_i_transport_r) = S ((S (ff_i_transport_r)) * d)) /\ exists ff_q_transport_r_decoded. z = ff_q_transport_r_decoded * S ((S (ff_i_transport_r)) * d) + (a + ff_i_transport_r)))) -> forall i x. (exists h. h + S i = l) -> (((exists ff_h_range_transport_x. ff_h_range_transport_x + S (x) = S ((S (i)) * c)) /\ exists ff_q_range_transport_x. b = ff_q_range_transport_x * S ((S (i)) * c) + (x))) -> (((exists ff_h_range_transport_y. ff_h_range_transport_y + S (x) = S ((S (i)) * d)) /\ exists ff_q_range_transport_y. z = ff_q_range_transport_y * S ((S (i)) * d) + (x)))Structural proof guide
Two Range codes preserve every decoded entry extensionally.
Direct prerequisites: beta_range_entry_eq. The authored body proceeds by intermediate claims (1), equality transport (2).
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are hypotheses of this body receipt. The focused endpoint audits separately check the complete empty-context certificates.
- 0001
intro b - 0002
intro c - 0003
intro z - 0004
intro d - 0005
intro a - 0006
intro l - 0007
intro hleft - 0008
intro hright - 0009
intro i - 0010
intro x - 0011
intro hi - 0012
intro hx - 0013
have hxa : x = a + i - 0014
specialize beta_range_entry_eq b - 0015
specialize beta_range_entry_eq c - 0016
specialize beta_range_entry_eq a - 0017
specialize beta_range_entry_eq l - 0018
specialize beta_range_entry_eq i - 0019
specialize beta_range_entry_eq x - 0020
apply beta_range_entry_eq - 0021
exact hleft - 0022
exact hi - 0023
exact hx - 0024
rewrite hxa - 0025
rewrite hxa - 0026
specialize hright i - 0027
apply hright - 0028
exact hi