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Proof step 4 from proof replay-lpt-at (previous step)

lpt[m] = mklp(m0, m1, lpf, m2), m < # lpt, m < n, n ≤ # lpt ⊦ replay-lpt(lpt, nx, n)[m] = (lpf = LP_FREE ∨ m ∈ nx ⊃ mklp(m0, m1, lpf, m2) ;(lpf = LP_INDEX_NODES ∧ m0 ≠ 0 ⊃ mklp(m0, LEB_SIZE, LP_INDEX_NODES, m2);(m0 = 0 ⊃ mklp(0, 0, LP_FREE, m2);mklp(m0, m1, lpf, m2))) )

User applied rule structural induction

And obtained the following new goals

Proof step 5:
lpt[m] = mklp(m0, m1, lpf, m2), m < n0 +1, m < # lpt, n0 +1 ≤ # lpt, ∀ lpt, m, m0, m1, lpf, m2, nx. lpt[m] = mklp(m0, m1, lpf, m2) ∧ m < # lpt ∧ m < n0 ∧ n0 ≤ # lpt → replay-lpt(lpt, nx, n0)[m] = (lpf = LP_FREE ∨ m ∈ nx ⊃ mklp(m0, m1, lpf, m2) ;(lpf = LP_INDEX_NODES ∧ m0 ≠ 0 ⊃ mklp(m0, LEB_SIZE, LP_INDEX_NODES, m2);(m0 = 0 ⊃ mklp(0, 0, LP_FREE, m2);mklp(m0, m1, lpf, m2))) ) ⊦ replay-lpt(lpt, nx, n0 +1)[m] = (lpf = LP_FREE ∨ m ∈ nx ⊃ mklp(m0, m1, lpf, m2) ;(lpf = LP_INDEX_NODES ∧ m0 ≠ 0 ⊃ mklp(m0, LEB_SIZE, LP_INDEX_NODES, m2);(m0 = 0 ⊃ mklp(0, 0, LP_FREE, m2);mklp(m0, m1, lpf, m2))) )

Rule argument

indvar: n

Additional information

Used simplifier rules: replay-lpt-base: ⊦ replay-lpt(lpt, nx, 0) = lpt;%nat freely generated by 0, +1;;% ⊦ 0 ≤ m; (s)% ⊦ ¬ m < 0; (s)