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Proof step 7 from proof lpt-ram-flash-cleanup (previous step)

# lpt0 = # lpt1, lpt0[n] = mklp(m2, m3, LP_GROUP_NODES, m4), lpt1.map(λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx);lp))[n] = mklp(m, m0, LP_GROUP_NODES, m1), n < # lpt1, ∀ n. n < # lpt1 ∧ lpt0[n].flags = LP_GROUP_NODES ∧ lpt1[n].flags = LP_GROUP_NODES → lpt1[n].size = lpt0[n].size ⊦ m0 = m3

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ lpt.map(lptfun)[n] = (n < # lpt ⊃ lptfun(lpt[n]);lpt[n])
Proof step 9:
# lpt0 = # lpt1, (n < # lpt1 ⊃ (lpt1[n].ref-size = 0 ∧ lpt1[n].flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lpt1[n].gcheapidx);lpt1[n]);lpt1[n]) = mklp(m, m0, LP_GROUP_NODES, m1), lpt0[n] = mklp(m2, m3, LP_GROUP_NODES, m4), n < # lpt1, ∀ n. n < # lpt1 ∧ lpt0[n].flags = LP_GROUP_NODES ∧ lpt1[n].flags = LP_GROUP_NODES → lpt1[n].size = lpt0[n].size ⊦ m0 = m3

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 ), lpt1] 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 ), lpt1