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Proof step 25 from proof abs-istore-crash (previous step)

# avol0 = # lpt, # lpt0 = # lpt, (lpf2 = LP_FREE ∨ n ∈ nx ⊃ mklp(m12, m13, lpf2, m14) ;(lpf2 = LP_INDEX_NODES ∧ m12 ≠ 0 ⊃ mklp(m12, LEB_SIZE, LP_INDEX_NODES, m14);(m12 = 0 ⊃ mklp(0, 0, LP_FREE, m14);mklp(m12, m13, lpf2, m14))) ) = mklp(m0, m1, lpf, m2), lpf0 = LP_INDEX_NODES ↔ n ∈ istore, n ∈ istore0 ↔ lpf1 = LP_INDEX_NODES ∧ m9 ≠ 0, n ∈ gstore0 ↔ lpf1 = LP_GROUP_NODES ∧ m9 ≠ 0, istore0[n] = indexblock(indx1, lax2, m8), istore[n] = indexblock(indx0, lax0, m3), remove-refsize0(crash(istore, istore0))[n] = indexblock(indx, lax, m), lpt[n] = mklp(m4, m5, lpf0, m6), gstore0[n] = groupblock(gndx, lax1, m7), lpt0[n] = mklp(m9, m10, lpf1, m11), lpt0.mapIndices(elems nx, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx))[n] = mklp(m12, m13, lpf2, m14), dom istore ∩ elems nx = ∅, n < # lpt, synced(avol0), avol1 ↓ avol0, istore0 ⊑ istore, n ∈ istore → abs-leb(avol0[n], indexblock(indx0, lax0, m3), mklp(m3, m5, lpf0, m6)) ∧ m4 = m3, n ∈ istore0 → m9 = m8, n ∈ gstore0 → m9 = m7, lpf1 = LP_FREE → m9 = 0, ∀ n. n < # lpt ∧ lpt0[n].flags = LP_FREE → lpt0[n].ref-size = 0 ⊦ (lpf = LP_INDEX_NODES ↔ n ∈ remove-refsize0(crash(istore, istore0))) ∧ (n ∈ remove-refsize0(crash(istore, istore0)) → abs-leb(avol1[n], indexblock(indx, lax, m), mklp(m, m1, lpf, m2)) ∧ m0 = m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ lpt.mapIndices(ns, lptfun)[n] = (n ∈ ns ∧ n < # lpt ⊃ lptfun(lpt[n]);lpt[n])
Proof step 27:
# lpt0 = # lpt, # avol0 = # lpt, (n ∈ elems nx ∧ n < # lpt0 ⊃ mklp(lpt0[n].ref-size, LEB_SIZE, LP_GROUP_NODES, lpt0[n].gcheapidx);lpt0[n]) = mklp(m12, m13, lpf2, m14), (lpf2 = LP_FREE ∨ n ∈ nx ⊃ mklp(m12, m13, lpf2, m14) ;(lpf2 = LP_INDEX_NODES ∧ m12 ≠ 0 ⊃ mklp(m12, LEB_SIZE, LP_INDEX_NODES, m14);(m12 = 0 ⊃ mklp(0, 0, LP_FREE, m14);mklp(m12, m13, lpf2, m14))) ) = mklp(m0, m1, lpf, m2), n ∈ gstore0 ↔ lpf1 = LP_GROUP_NODES ∧ m9 ≠ 0, n ∈ istore0 ↔ lpf1 = LP_INDEX_NODES ∧ m9 ≠ 0, lpf0 = LP_INDEX_NODES ↔ n ∈ istore, lpt0[n] = mklp(m9, m10, lpf1, m11), gstore0[n] = groupblock(gndx, lax1, m7), lpt[n] = mklp(m4, m5, lpf0, m6), remove-refsize0(crash(istore, istore0))[n] = indexblock(indx, lax, m), istore[n] = indexblock(indx0, lax0, m3), istore0[n] = indexblock(indx1, lax2, m8), dom istore ∩ elems nx = ∅, n < # lpt, synced(avol0), avol1 ↓ avol0, istore0 ⊑ istore, lpf1 = LP_FREE → m9 = 0, n ∈ gstore0 → m9 = m7, n ∈ istore0 → m9 = m8, n ∈ istore → abs-leb(avol0[n], indexblock(indx0, lax0, m3), mklp(m3, m5, lpf0, m6)) ∧ m4 = m3, ∀ n. n < # lpt ∧ lpt0[n].flags = LP_FREE → lpt0[n].ref-size = 0 ⊦ (lpf = LP_INDEX_NODES ↔ n ∈ remove-refsize0(crash(istore, istore0))) ∧ (n ∈ remove-refsize0(crash(istore, istore0)) → abs-leb(avol1[n], indexblock(indx, lax, m), mklp(m, m1, lpf, m2)) ∧ m0 = m)

Rule argument

spec: array-indices, inst: lp-array name: mapindices-at seq: ⊦ lpt.mapIndices(ns, lptfun)[n] = (n ∈ ns ∧ n < # lpt ⊃ lptfun(lpt[n]);lpt[n]) subst: [n, lptfun, ns, lpt] → [n, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx), elems nx, lpt0] flags: <all paths>

Additional information

Used terms: n, λ lp. mklp(lp.ref-size, LEB_SIZE, LP_GROUP_NODES, lp.gcheapidx), elems nx, lpt0