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Proof step 21 from proof id-idx-abs-gstore (previous step)

# lpt1 = # lpt0, n < # lpt0 ∧ lpf0 = LP_GROUP_NODES ↔ n ∈ gstore, lpt0[n] = mklp(m0, m1, lpf, m2), gstore[n] = groupblock(gndx, lax, m), lpt1[n] = mklp(m3, m4, lpf0, m5), n ∈ gstore → m3 = m, n < # lpt0 → m0 = m3 ∧ m1 = m4 ∧ lpf = lpf0, n ∈ gstore ∧ ¬ n ∈ ginval → avol[n].mapped? ∧ abs-nodes(avol[n].data, gndx, lax, m4 = LEB_SIZE) ∧ (m4 ≠ LEB_SIZE → m4 = # avol[n].data) ⊦ (n < # lpt0 ∧ lpf = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], groupblock(gndx, lax, m), mklp(m0, m1, lpf, m2))) ∧ (n ∈ gstore → m0 = m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ abs-leb(aleb, gblock, lp) ↔ aleb.mapped? ∧ abs-nodes(aleb.data, gblock.gndlist, gblock.ladrlist, lp.size = LEB_SIZE) ∧ (lp.size ≠ LEB_SIZE → lp.size = # aleb.data)
Proof step 23:
# lpt1 = # lpt0, n < # lpt0 ∧ lpf0 = LP_GROUP_NODES ↔ n ∈ gstore, lpt1[n] = mklp(m3, m4, lpf0, m5), gstore[n] = groupblock(gndx, lax, m), lpt0[n] = mklp(m0, m1, lpf, m2), n ∈ gstore ∧ ¬ n ∈ ginval → avol[n].mapped? ∧ abs-nodes(avol[n].data, gndx, lax, m4 = LEB_SIZE) ∧ (m4 ≠ LEB_SIZE → m4 = # avol[n].data), n < # lpt0 → m0 = m3 ∧ m1 = m4 ∧ lpf = lpf0, n ∈ gstore → m3 = m ⊦ (n < # lpt0 ∧ lpf = LP_GROUP_NODES ↔ n ∈ gstore) ∧ ( n ∈ gstore ∧ ¬ n ∈ ginval → avol[n].mapped? ∧ abs-nodes(avol[n].data, groupblock(gndx, lax, m).gndlist, groupblock(gndx, lax, m).ladrlist, mklp(m0, m1, lpf, m2).size = LEB_SIZE) ∧ (mklp(m0, m1, lpf, m2).size ≠ LEB_SIZE → mklp(m0, m1, lpf, m2).size = # avol[n].data)) ∧ (n ∈ gstore → m0 = m)

Rule argument

spec: abs-leb, inst: encoding-group-node name: abs-leb-def seq: ⊦ abs-leb(aleb, gblock, lp) ↔ aleb.mapped? ∧ abs-nodes (aleb.data, gblock.gndlist, gblock.ladrlist, lp.size = LEB_SIZE) ∧ (lp.size ≠ LEB_SIZE → lp.size = # aleb.data) subst: [lp, gblock, aleb] → [mklp(m0, m1, lpf, m2), groupblock(gndx, lax, m), avol[n]] flags: <all paths>

Additional information

Used terms: mklp(m0, m1, lpf, m2), groupblock(gndx, lax, m), avol[n]