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Proof step 3 from proof payload-keys-0 (previous step)

key ∈ payload(zbrar, 0, nused), nused ≤ # zbrar ⊦ key ∈ keys(zbrar, 0, nused)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ key ∈ payload(zbrar, n, nused) ∧ nused + n ≤ # zbrar → key ∈ keys(zbrar, n, nused)

Rule argument

spec: <toplevel> name: payload-keys seq: ⊦ key ∈ payload(zbrar, n, nused) ∧ nused + n ≤ # zbrar → key ∈ keys(zbrar, n, nused) subst: [nused, n, zbrar, key] → [nused, 0, zbrar, key] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: nused, 0, zbrar, key