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Proof step 8 from proof monls-append2 (previous step)

nl0[n + 1] ≤ nl0[n], 1 + n < # nl0, ∀ n. 1 + n < # nl0 + # nl → (nl + nl0)[n] < (nl + nl0)[n + 1] ⊦ nl0 = []

User applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: # nl + n abort: F discard: T computed: F

Additional information

Used simplifier rules: l: ⊦ m + n < m + n0 ↔ n < n0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%get-append-grt-02: ⊦ (nl + nl0)[n + # nl] = nl0[n]; from specification list-del[natstream]%a: ⊦ (nl + nl0) + nl1 = nl + nl0 + nl1; from specification list[natstream]%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat Used terms: # nl + n