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Proof step 9 from proof abs-gstore-replay-lpt-unchanged (previous step)

# lpt = # avol1, # avol0 = # avol1, (n ∈ nx ∨ ¬ n ∈ ginval ⊃ groupblock(gstore[n].gndlist, gstore[n].ladrlist, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0));gstore0[n]) = groupblock(gndx, lax, m), replay-lpt(lpt, nx, # avol1)[n] = mklp(m0, m1, lpf, m2), n < # avol1 ∧ (n ∈ nx ∨ lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n], ∀ n. (n < # avol1 ∧ replay-lpt(lpt, nx, # avol1)[n].flags = LP_GROUP_NODES ↔ n ∈ crash(gstore, gstore0, ginval, nx)) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol1[n], crash(gstore, gstore0, ginval, nx)[n], replay-lpt(lpt, nx, # avol1)[n])) ∧ ( n ∈ crash(gstore, gstore0, ginval, nx) → replay-lpt(lpt, nx, # avol1)[n].ref-size = (n ∈ nx ∨ ¬ n ∈ ginval ⊃ groupblock(gstore[n].gndlist, gstore[n].ladrlist, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0));gstore0[n]).ref-size) ⊦ (n < # avol1 ∧ lpf = LP_GROUP_NODES ↔ n ∈ crash(gstore, gstore0, ginval, nx)) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], crash(gstore, gstore0, ginval, nx)[n], mklp(m0, m1, lpf, m2))) ∧ (n ∈ crash(gstore, gstore0, ginval, nx) → m0 = m)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
# avol0 = # avol1, # lpt = # avol1, (n ∈ nx ∨ ¬ n ∈ ginval ⊃ groupblock(gstore[n].gndlist, gstore[n].ladrlist, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0));gstore0[n]) = groupblock(gndx, lax, m), replay-lpt(lpt, nx, # avol1)[n] = mklp(m0, m1, lpf, m2), lpt[n] = mklp(m3, m4, lpf0, m5), n < # avol1 ∧ (n ∈ nx ∨ m3 ≠ 0 ∨ lpf0 = LP_FREE) → avol0[n] = avol1[n], ∀ n. (n < # avol1 ∧ replay-lpt(lpt, nx, # avol1)[n].flags = LP_GROUP_NODES ↔ n ∈ crash(gstore, gstore0, ginval, nx)) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol1[n], crash(gstore, gstore0, ginval, nx)[n], replay-lpt(lpt, nx, # avol1)[n])) ∧ ( n ∈ crash(gstore, gstore0, ginval, nx) → replay-lpt(lpt, nx, # avol1)[n].ref-size = (n ∈ nx ∨ ¬ n ∈ ginval ⊃ groupblock(gstore[n].gndlist, gstore[n].ladrlist, (n ∈ gstore0 ⊃ gstore0[n].ref-size;0));gstore0[n]).ref-size) ⊦ (n < # avol1 ∧ lpf = LP_GROUP_NODES ↔ n ∈ crash(gstore, gstore0, ginval, nx)) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], crash(gstore, gstore0, ginval, nx)[n], mklp(m0, m1, lpf, m2))) ∧ (n ∈ crash(gstore, gstore0, ginval, nx) → m0 = m)

Rule argument

spec: lprops name: elim seq: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1) subst: [lp, m, m0, lpf, m1] → [lpt[n], m4, m5, lpf0, m6]

Additional information

Used simplifier rules: ⊦ ((m = lp.ref-size ∧ m0 = lp.size) ∧ lpf = lp.flags) ∧ m1 = lp.gcheapidx ↔ lp = mklp(m, m0, lpf, m1); (elim) Used terms: lpt[n], m4, m5, lpf0, m6