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Proof step 19 from proof abs-gstore-replay-lpt-unchanged (previous step)

# avol0 = # avol1, # lpt = # avol1, (lpf0 = LP_FREE ∨ n ∈ nx ⊃ mklp(m3, m4, lpf0, m5) ;(lpf0 = LP_INDEX_NODES ∧ m3 ≠ 0 ⊃ mklp(m3, LEB_SIZE, LP_INDEX_NODES, m5);(m3 = 0 ⊃ mklp(0, 0, LP_FREE, m5);mklp(m3, m4, lpf0, m5))) ) = mklp((n ∈ gstore0 ⊃ gstore0[n].ref-size;0), m1, LP_GROUP_NODES, m2), gstore[n] = groupblock(gndx, lax, m), lpt[n] = mklp(m3, m4, lpf0, m5), n < # avol1, abs-leb(avol1[n], groupblock(gndx, lax, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0)), mklp((n ∈ gstore0 ⊃ gstore0[n].ref-size;0), m1, LP_GROUP_NODES, m2)), n ∈ gstore, n ∈ nx ∨ m3 ≠ 0 ∨ lpf0 = LP_FREE → avol0[n] = avol1[n] ⊦ n ∈ ginval, avol0[n].mapped? ∧ abs-nodes(avol0[n].data, crash(gstore, gstore0, ginval, nx)[n].gndlist, crash(gstore, gstore0, ginval, nx)[n].ladrlist, m1 = LEB_SIZE) ∧ (m1 ≠ LEB_SIZE → m1 = # avol0[n].data)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
# lpt = # avol1, # avol0 = # avol1, (lpf0 = LP_FREE ∨ n ∈ nx ⊃ mklp(m3, m4, lpf0, m5) ;(lpf0 = LP_INDEX_NODES ∧ m3 ≠ 0 ⊃ mklp(m3, LEB_SIZE, LP_INDEX_NODES, m5);(m3 = 0 ⊃ mklp(0, 0, LP_FREE, m5);mklp(m3, m4, lpf0, m5))) ) = mklp((n ∈ gstore0 ⊃ gstore0[n].ref-size;0), m1, LP_GROUP_NODES, m2), lpt[n] = mklp(m3, m4, lpf0, m5), gstore[n] = groupblock(gndx, lax, m), crash(gstore, gstore0, ginval, nx)[n] = groupblock(gndx0, lax0, m0), n < # avol1, abs-leb(avol1[n], groupblock(gndx, lax, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0)), mklp((n ∈ gstore0 ⊃ gstore0[n].ref-size;0), m1, LP_GROUP_NODES, m2)), n ∈ gstore, n ∈ nx ∨ m3 ≠ 0 ∨ lpf0 = LP_FREE → avol0[n] = avol1[n] ⊦ n ∈ ginval, avol0[n].mapped? ∧ abs-nodes(avol0[n].data, gndx0, lax0, m1 = LEB_SIZE) ∧ (m1 ≠ LEB_SIZE → m1 = # avol0[n].data)

Rule argument

spec: ablock, inst: group-store name: elim seq: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m) subst: [gblock, gndx, lax, m, m0] → [crash(gstore, gstore0, ginval, nx)[n], gndx0, lax0, m1, m2]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: crash(gstore, gstore0, ginval, nx)[n], gndx0, lax0, m1, m2