BT001D

lt_of_lt_of_le

Stable · empty-context checked

Strict order followed by weak order remains strict.

Exact expanded PA statement

forall a b c. (exists k. k + S a = b) -> (exists k. k + b = c) -> exists k. k + S a = c

Structural proof guide

Strict order followed by weak order remains strict.

Direct prerequisites: le_trans. The authored body proceeds by direct introduction and elimination.

Proof neighborhood

Direct dependencies

BT000F le_trans

Direct dependents

BT003K prime_divisor_exists_up_to BT00R2 ceil_div_six_functional BT00RC floor_sqrt_monotone BT00RF ceil_div_six_le_of_upper BT00TY mul_lt_mul_right_nonzero BT00UX primorial_factor_prefix_restrict_add BT00XK pow_tail_strict_of_square BT00XO prime_power_quotient_zero_of_exponent_gt BT00YA prime_square_tail_of_two_three_range BT00YF division_three_scaled_upper_of_quotient_lt BT00YH floor_sqrt_above_root_power_two_strict BT010B floor_sqrt_two_le_of_two_lt BT010E division_quotient_lower_of_scaled_le BT010Q prime_contribution_prefix_restrict_add BT0115 bertrand_eventually_closed_upper

Formal native tactic body

Dependencies are hypotheses of this body receipt. The focused endpoint audits separately check the complete empty-context certificates.

  1. 0001intro a
  2. 0002intro b
  3. 0003intro c
  4. 0004intro hab
  5. 0005intro hbc
  6. 0006specialize le_trans (S a)
  7. 0007specialize le_trans b
  8. 0008specialize le_trans c
  9. 0009apply le_trans
  10. 0010exact hab
  11. 0011exact hbc