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Proof step 5 from proof abs-istore-replay-lpt-unchanged (previous step)

# lpt = # avol1, # avol0 = # avol1, ∀ n. (n < # avol1 ∧ replay-lpt(lpt, nx, # avol1)[n].flags = LP_INDEX_NODES ↔ n ∈ remove-refsize0(istore)) ∧ ( n ∈ remove-refsize0(istore) → abs-leb(avol1[n], remove-refsize0(istore)[n], replay-lpt(lpt, nx, # avol1)[n]) ∧ replay-lpt(lpt, nx, # avol1)[n].ref-size = remove-refsize0(istore)[n].ref-size), ∀ n. n < # avol1 ∧ (n ∈ nx ∨ lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n] ⊦ (n < # avol1 ∧ replay-lpt(lpt, nx, # avol1)[n].flags = LP_INDEX_NODES ↔ n ∈ remove-refsize0(istore)) ∧ ( n ∈ remove-refsize0(istore) → abs-leb(avol0[n], remove-refsize0(istore)[n], replay-lpt(lpt, nx, # avol1)[n]) ∧ replay-lpt(lpt, nx, # avol1)[n].ref-size = remove-refsize0(istore)[n].ref-size)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
# avol0 = # avol1, # lpt = # avol1, remove-refsize0(istore)[n] = indexblock(indx, lax, m), ∀ n. 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_INDEX_NODES ↔ n ∈ remove-refsize0(istore)) ∧ ( n ∈ remove-refsize0(istore) → abs-leb(avol1[n], remove-refsize0(istore)[n], replay-lpt(lpt, nx, # avol1)[n]) ∧ replay-lpt(lpt, nx, # avol1)[n].ref-size = remove-refsize0(istore)[n].ref-size) ⊦ (n < # avol1 ∧ replay-lpt(lpt, nx, # avol1)[n].flags = LP_INDEX_NODES ↔ n ∈ remove-refsize0(istore)) ∧ ( n ∈ remove-refsize0(istore) → abs-leb(avol0[n], remove-refsize0(istore)[n], replay-lpt(lpt, nx, # avol1)[n]) ∧ replay-lpt(lpt, nx, # avol1)[n].ref-size = m)

Rule argument

spec: ablock, inst: index-store name: elim seq: ⊦ (indx = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indx, lax, m) subst: [iblock, indx, lax, m, m0, m1, boolvar] → [remove-refsize0(istore)[n], indx, lax, m, m0, m1, boolvar]

Additional information

Used simplifier rules: ⊦ (indx = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indx, lax, m); (elim) Used terms: remove-refsize0(istore)[n], indx, lax, m, m0, m1, boolvar