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Proof step 6 from proof replay-log-append-one (previous step)

lpt[n] = mklp(m, m0, lpf, m1) ⊦ n ∈ nx, # lpt.mapIndices(elems nx ++ n, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx)) = # lpt.mapIndices(elems nx, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx))[n, mklp(m, LEB_SIZE, LP_GROUP_NODES, m1)] ∧ (∀ n0. n0 < # lpt.mapIndices(elems nx ++ n, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx)) → lpt.mapIndices(elems nx ++ n, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx))[n0] = lpt.mapIndices(elems nx, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx))[n, mklp(m, LEB_SIZE, LP_GROUP_NODES, m1)][n0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
lpt[n] = mklp(m, m0, lpf, m1), n0 < # lpt ⊦ lpt.mapIndices(elems nx ++ n, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx))[n0] = lpt.mapIndices(elems nx, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx))[n, mklp(m, LEB_SIZE, LP_GROUP_NODES, m1)][n0], n ∈ nx

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ # lpt[n, lp] = # lpt; (s)% ⊦ # lpt.mapIndices(ns, lptfun) = # lpt; (s)