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

# lpt = # avol, abs-gstore(avol, lpt, gstore, ginval) ⊦ abs-gstore(avol[n, aleb], lpt[n, lp], gstore[n, gblock], ginval) ↔ n < # lpt ∧ ((lpt[n].flags = LP_GROUP_NODES → lpt[n].ref-size = gstore[n].ref-size) → lp.ref-size = gblock.ref-size ∧ lp.flags = LP_GROUP_NODES) ∧ (¬ n ∈ ginval ∧ (lpt[n].flags = LP_GROUP_NODES → abs-leb(avol[n], gstore[n], lpt[n])) → abs-leb(aleb, gblock, lp))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# lpt = # avol, ∀ n. (n < # avol ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size) ⊦ (∀ n0. (n0 < # avol ∧ lpt[n, lp][n0].flags = LP_GROUP_NODES ↔ n0 ∈ gstore[n, gblock]) ∧ (n0 ∈ gstore[n, gblock] ∧ ¬ n0 ∈ ginval → abs-leb(avol[n, aleb][n0], gstore[n, gblock][n0], lpt[n, lp][n0])) ∧ (n0 ∈ gstore[n, gblock] → lpt[n, lp][n0].ref-size = gstore[n, gblock][n0].ref-size)) ↔ n < # avol ∧ ((lpt[n].flags = LP_GROUP_NODES → lpt[n].ref-size = gstore[n].ref-size) → lp.ref-size = gblock.ref-size ∧ lp.flags = LP_GROUP_NODES) ∧ (¬ n ∈ ginval ∧ (lpt[n].flags = LP_GROUP_NODES → abs-leb(avol[n], gstore[n], lpt[n])) → abs-leb(aleb, gblock, lp))

Rule argument

Additional information

Used simplifier rules: abs-gstore-def: ⊦ abs-gstore(avol, lpt, gstore, ginval) ↔ (∀ n. (n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ ( n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size));% ⊦ # lpt[n, lp] = # lpt; (s)