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Proof step 2 from proof abs-istore-reduce-write-idcircle (previous step)

# lpt = # avol0, abs-istore(avol0, lpt, istore), id○(avol1, avol0, n) ⊦ abs-istore(avol1, lpt[n, lp], istore[n, iblock]) ↔ n < # lpt ∧ ((lpt[n].flags = LP_INDEX_NODES → lpt[n].ref-size = istore[n].ref-size) → lp.ref-size = iblock.ref-size ∧ lp.flags = LP_INDEX_NODES) ∧ ((lpt[n].flags = LP_INDEX_NODES → abs-leb(avol0[n], istore[n], lpt[n])) → abs-leb(avol1[n], iblock, lp))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# lpt = # avol0, # avol1 = # avol0, id○(avol1, avol0, n), ∀ n. (n < # avol0 ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ (n ∈ istore → abs-leb(avol0[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size) ⊦ (∀ n0. (n0 < # avol0 ∧ lpt[n, lp][n0].flags = LP_INDEX_NODES ↔ n0 ∈ istore[n, iblock]) ∧ ( n0 ∈ istore[n, iblock] → abs-leb(avol1[n0], istore[n, iblock][n0], lpt[n, lp][n0]) ∧ lpt[n, lp][n0].ref-size = istore[n, iblock][n0].ref-size)) ↔ n < # avol0 ∧ ((lpt[n].flags = LP_INDEX_NODES → lpt[n].ref-size = istore[n].ref-size) → lp.ref-size = iblock.ref-size ∧ lp.flags = LP_INDEX_NODES) ∧ ((lpt[n].flags = LP_INDEX_NODES → abs-leb(avol0[n], istore[n], lpt[n])) → abs-leb(avol1[n], iblock, lp))

Rule argument

Additional information

Used simplifier rules: abs-istore-def: ⊦ abs-istore(avol, lpt, istore) ↔ (∀ n. (n < # lpt ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ ( n ∈ istore → abs-leb(avol[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size));%idexcept-size: ⊦ id○(avol, avol0, n) → # avol = # avol0; (forward) from specification array-copy[avolume]% ⊦ # lpt[n, lp] = # lpt; (s)