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Proof step 11 from proof abs-istore-reduce-write-idcircle (previous step)

# avol1 = # avol0, # lpt = # avol0, istore[n] = indexblock(indx0, lax0, m3), lpt[n] = mklp(m4, m5, lpf0, m6), id○(avol1, avol0, n), ∀ n. (n < # avol0 ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ (n ∈ istore → abs-leb(avol0[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size) ⊦ (∀ n0. (n0 < # avol0 ∧ lpt[n, mklp(m0, m1, lpf, m2)][n0].flags = LP_INDEX_NODES ↔ n0 ∈ istore[n, indexblock(indx, lax, m)]) ∧ ( n0 ∈ istore[n, indexblock(indx, lax, m)] → abs-leb(avol1[n0], istore[n, indexblock(indx, lax, m)][n0], lpt[n, mklp(m0, m1, lpf, m2)][n0]) ∧ lpt[n, mklp(m0, m1, lpf, m2)][n0].ref-size = istore[n, indexblock(indx, lax, m)][n0].ref-size)) ↔ n < # avol0 ∧ ((lpf0 = LP_INDEX_NODES → m4 = m3) → m0 = m ∧ lpf = LP_INDEX_NODES) ∧ ( (lpf0 = LP_INDEX_NODES → abs-leb(avol0[n], indexblock(indx0, lax0, m3), mklp(m4, m5, LP_INDEX_NODES, m6))) → abs-leb(avol1[n], indexblock(indx, lax, m), mklp(m0, m1, lpf, m2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ id○(avol, avol0, n) ↔ # avol = # avol0 ∧ (∀ m. m < # avol ∧ m ≠ n → avol[m] = avol0[m])
Proof step 13:
# lpt = # avol0, # avol1 = # avol0, lpt[n] = mklp(m4, m5, lpf0, m6), istore[n] = indexblock(indx0, lax0, m3), ∀ n. (n < # avol0 ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ (n ∈ istore → abs-leb(avol0[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size), ∀ m. m < # avol1 ∧ m ≠ n → avol1[m] = avol0[m] ⊦ (∀ n0. (n0 < # avol0 ∧ lpt[n, mklp(m0, m1, lpf, m2)][n0].flags = LP_INDEX_NODES ↔ n0 ∈ istore[n, indexblock(indx, lax, m)]) ∧ ( n0 ∈ istore[n, indexblock(indx, lax, m)] → abs-leb(avol1[n0], istore[n, indexblock(indx, lax, m)][n0], lpt[n, mklp(m0, m1, lpf, m2)][n0]) ∧ lpt[n, mklp(m0, m1, lpf, m2)][n0].ref-size = istore[n, indexblock(indx, lax, m)][n0].ref-size)) ↔ n < # avol0 ∧ ((lpf0 = LP_INDEX_NODES → m4 = m3) → m0 = m ∧ lpf = LP_INDEX_NODES) ∧ ( (lpf0 = LP_INDEX_NODES → abs-leb(avol0[n], indexblock(indx0, lax0, m3), mklp(m4, m5, LP_INDEX_NODES, m6))) → abs-leb(avol1[n], indexblock(indx, lax, m), mklp(m0, m1, lpf, m2)))

Rule argument

spec: array-copy, inst: avolume name: Idexcept seq: ⊦ id○(avol, avol0, n) ↔ # avol = # avol0 ∧ (∀ m. m < # avol ∧ m ≠ n → avol[m] = avol0[m]) subst: [n, avol0, avol] → [n, avol0, avol1] flags: <all paths>

Additional information

Used terms: n, avol0, avol1