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Proof step 14 from proof abs-gstore-cleanup-lpt (previous step)

# lpt = # avol1, # avol0 = # avol1, lpf0 = LP_GROUP_NODES ↔ n ∈ gstore, lpt.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[n] = mklp(m0, m1, lpf, m2), remove-refsize0(gstore)[n] = groupblock(gndx, lax, m), gstore[n] = groupblock(gndx0, lax0, m3), lpt[n] = mklp(m4, m5, lpf0, m6), dom remove-refsize0(gstore) ∩ ginval = ∅, n < # avol1, n ∈ gstore → m4 = m3, n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], groupblock(gndx0, lax0, m3), mklp(m4, m5, lpf0, m6)), ∀ n. n < # avol1 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n], ¬(lpf = LP_GROUP_NODES ↔ n ∈ remove-refsize0(gstore)) ∨ ¬(n ∈ remove-refsize0(gstore) → abs-leb(avol1[n], groupblock(gndx, lax, m), mklp(m0, m1, lpf, m2))) ∨ ¬(n ∈ remove-refsize0(gstore) → m0 = m) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ lpt.map(lptfun)[n] = (n < # lpt ⊃ lptfun(lpt[n]);lpt[n])
Proof step 16:
# avol0 = # avol1, # lpt = # avol1, (n < # lpt ⊃ (lpt[n].ref-size = 0 ∧ lpt[n].flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lpt[n].gcheapidx);lpt[n]);lpt[n]) = mklp(m0, m1, lpf, m2), lpf0 = LP_GROUP_NODES ↔ n ∈ gstore, lpt[n] = mklp(m4, m5, lpf0, m6), gstore[n] = groupblock(gndx0, lax0, m3), remove-refsize0(gstore)[n] = groupblock(gndx, lax, m), dom remove-refsize0(gstore) ∩ ginval = ∅, n < # avol1, n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], groupblock(gndx0, lax0, m3), mklp(m4, m5, lpf0, m6)), n ∈ gstore → m4 = m3, ∀ n. n < # avol1 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n], ¬(lpf = LP_GROUP_NODES ↔ n ∈ remove-refsize0(gstore)) ∨ ¬(n ∈ remove-refsize0(gstore) → abs-leb(avol1[n], groupblock(gndx, lax, m), mklp(m0, m1, lpf, m2))) ∨ ¬(n ∈ remove-refsize0(gstore) → m0 = m) ⊦

Rule argument

spec: array-indices, inst: lp-array name: map-at seq: ⊦ lpt.map(lptfun)[n] = (n < # lpt ⊃ lptfun(lpt[n]);lpt[n]) subst: [n, lptfun, lpt] → [n, λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx) ;lp ), lpt] flags: <all paths>

Additional information

Used terms: n, λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx) ;lp ), lpt