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Proof step 3 from proof abs-gstore-cleanup-lpt (previous step)

# lpt = # avol1, # avol0 = # avol1, dom remove-refsize0(gstore) ∩ ginval = ∅, ∀ n. n < # avol1 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n], ∀ n. (n < # avol1 ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size), ¬ ( n < # avol1 ∧ lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[n].flags = LP_GROUP_NODES ↔ n ∈ remove-refsize0(gstore)) ∨ ¬ ( n ∈ remove-refsize0(gstore) → abs-leb(avol1[n], remove-refsize0(gstore)[n], lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[n])) ∨ ¬ ( n ∈ remove-refsize0(gstore) → lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[n].ref-size = remove-refsize0(gstore)[n].ref-size) ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
# avol0 = # avol1, # lpt = # avol1, remove-refsize0(gstore)[n] = groupblock(gndx, lax, m), dom remove-refsize0(gstore) ∩ ginval = ∅, ∀ n. (n < # avol1 ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size), ∀ n. n < # avol1 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n], ¬ ( n < # avol1 ∧ lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[n].flags = LP_GROUP_NODES ↔ n ∈ remove-refsize0(gstore)) ∨ ¬ ( n ∈ remove-refsize0(gstore) → abs-leb(avol1[n], remove-refsize0(gstore)[n], lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[n])) ∨ ¬(n ∈ remove-refsize0(gstore) → lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[n].ref-size = m) ⊦

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] → [remove-refsize0(gstore)[n], gndx, lax, m]

Additional information

Used simplifier rules: ⊦ (gndx = gblock.gndlist ∧ lax = gblock.ladrlist) ∧ m = gblock.ref-size ↔ gblock = groupblock(gndx, lax, m); (elim) Used terms: remove-refsize0(gstore)[n], gndx, lax, m