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Proof step 2 from proof abs-istore-cleanup-lpt (previous step)

abs-istore(avol0, lpt, istore), avol-cleanup-lpt-unchanged(avol0, avol1, lpt) ⊦ ¬ abs-istore(avol1, cleanup-lpt(lpt), remove-refsize0(istore)) ↔ false

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# lpt = # avol1, # avol0 = # avol1, ∀ n. n < # avol1 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n], ∀ n. (n < # avol1 ∧ 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), ¬ ( 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_INDEX_NODES ↔ n ∈ remove-refsize0(istore)) ∨ ¬ ( n ∈ remove-refsize0(istore) → abs-leb(avol1[n], remove-refsize0(istore)[n], lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[n]) ∧ 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(istore)[n].ref-size) ⊦

Rule argument

Additional information

Used simplifier rules: cleanup-lpt: ⊦ cleanup-lpt(lpt) = lpt .map (λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx) ;lp ) );%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));%avol-cleanup-lpt-unchanged: ⊦ avol-cleanup-lpt-unchanged(avol0, avol1, lpt) ↔ # avol0 = # avol1 ∧ # avol0 = # lpt ∧ (∀ n. n < # avol0 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n]);% ⊦ # lpt.map(lptfun) = # lpt; (s)