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Proof step 9 from proof lpt-free-unref-cleanup-lpt (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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 simplifier rules: ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws) Used terms: n, λ lp. (lp.ref-size = 0 ∧ lp.flags ≠ LP_FREE ⊃ mklp(0, 0, LP_FREE, lp.gcheapidx) ;lp ), lpt