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Proof step 20 from proof abs-gstore-replay-lpt-unchanged (previous step)

# 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ 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 22:
# 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), crash(gstore, gstore0, ginval, nx)[n] = groupblock(gndx0, lax0, m0), gstore[n] = groupblock(gndx, lax, m), lpt[n] = mklp(m3, m4, lpf0, m5), avol1[n].mapped?, n < # avol1, abs-nodes (avol1[n].data, groupblock(gndx, lax, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0)).gndlist, groupblock(gndx, lax, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0)).ladrlist, mklp((n ∈ gstore0 ⊃ gstore0[n].ref-size;0), m1, LP_GROUP_NODES, m2).size = LEB_SIZE), n ∈ gstore, n ∈ nx ∨ m3 ≠ 0 ∨ lpf0 = LP_FREE → avol0[n] = avol1[n], mklp((n ∈ gstore0 ⊃ gstore0[n].ref-size;0), m1, LP_GROUP_NODES, m2).size ≠ LEB_SIZE → mklp((n ∈ gstore0 ⊃ gstore0[n].ref-size;0), m1, LP_GROUP_NODES, m2).size = # avol1[n].data ⊦ 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: 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 ((n ∈ gstore0 ⊃ gstore0[n].ref-size;0), m1, LP_GROUP_NODES, m2), groupblock(gndx, lax, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0)), avol1[n]] flags: <all paths>

Additional information

Used terms: mklp((n ∈ gstore0 ⊃ gstore0[n].ref-size;0), m1, LP_GROUP_NODES, m2), groupblock(gndx, lax, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0)), avol1[n]