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Proof step 16 from proof id-idx-write-both (previous step)

# lpt1 = # lpt0, lpt1[n, mklp(n0, n1, lpf, m2)][n3] = mklp(m3, m4, lpf1, m5), lpt0[n, mklp(n0, n1, lpf, n2)][n3] = mklp(m, m0, lpf0, m1), lpt0[n3] = mklp(m6, m7, lpf2, m8), lpt1[n3] = mklp(m6, m7, lpf2, m9), n3 < # lpt0 ⊦ m = m3 ∧ m0 = m4 ∧ lpf0 = lpf1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array, inst: gc-heap-base-index-array-base name: Put-other seq: ⊦ m ≠ n → lpt[n, lp][m] = lpt[m] subst: [m, lp, n, lpt] → [n3, mklp(n0, n1, lpf, m2), n, lpt1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≠ n → lpt[n, lp][m] = lpt[m]; (s)%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # lpt ⊦ lpt[m, lp][m] = lp; (s)% ⊦ m < # lpt → lpt[m, lp][m] = lp; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic Used terms: n3, mklp(n0, n1, lpf, m2), n, lpt1