[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 4 from proof replay-log-append-one (previous step)

lpt[n] = mklp(m, m0, lpf, m1) ⊦ 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)], n ∈ nx

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ lpt = lpt0 ↔ # lpt = # lpt0 ∧ (∀ n. n < # lpt → lpt[n] = lpt0[n])
Proof step 6:
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])

Rule argument

spec: array, inst: lp-array name: Extension seq: ⊦ lpt = lpt0 ↔ # lpt = # lpt0 ∧ (∀ n. n < # lpt → lpt[n] = lpt0[n]) subst: [lpt0, lpt] → [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) ], lpt .mapIndices (elems nx ++ n, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx) )] flags: <all paths>

Additional information

Used terms: 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) ], lpt .mapIndices (elems nx ++ n, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx) )