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Proof step 12 from proof abs-istore-set-refsize (previous step)

n5 < # lpt ∧ lpf0 = LP_INDEX_NODES ↔ n5 ∈ istore, istore[n5] = indexblock(indx1, lax1, m4), lpt[n, mklp(m0, n1, LP_INDEX_NODES, n2)][n5] = mklp(m1, m2, lpf, m3), istore[n] = indexblock(indx, lax, n3), lpt[n] = mklp(n0, n1, LP_INDEX_NODES, n4), istore[n, indexblock(indx, lax, m0)][n5] = indexblock(indx0, lax0, m), lpt[n5] = mklp(m5, m6, lpf0, m7), n ∈ istore, n5 ∈ istore → abs-leb(avol[n5], indexblock(indx1, lax1, m4), mklp(m4, m6, lpf0, m7)) ∧ m5 = m4 ⊦ (n5 < # lpt ∧ lpf = LP_INDEX_NODES ↔ n5 ∈ istore[n, indexblock(indx, lax, m0)]) ∧ (n5 ∈ istore[n, indexblock(indx, lax, m0)] → abs-leb(avol[n5], indexblock(indx0, lax0, m), mklp(m, m2, lpf, m3)) ∧ m1 = m)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: index-store-ablock-store-nat-store name: At-other seq: ⊦ n ≠ n0 → istore[n0, iblock][n] = istore[n] subst: [n, iblock, n0, istore] → [n5, indexblock(indx, lax, m0), n, istore] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≠ n → lpt[n, lp][m] = lpt[m]; (s)% ⊦ n ≠ n0 → (n ∈ istore[n0, iblock] ↔ n ∈ istore); (s)%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)%⊦ indexblock(indx, lax, m) = indexblock(indx0, lax0, m0) ↔ indx = indx0 ∧ lax = lax0 ∧ m = m0; (ws) Used terms: n5, indexblock(indx, lax, m0), n, istore