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Proof step 10 from proof to-adrs-drop (previous step)

∀ n, m. dropn(n, lax0.to-adr(m)) = dropn(n, lax0).to-adr(m) ⊦ dropn(m2, lax0.to-adr(m)) = dropn(m2 + 1, @(m0, m1) ' + lax0).to-adr(m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ n ≠ 0 → dropn(n, lax) = (lax = [] ⊃ [];dropn(n - 1, lax.tail))
Proof step 12:
∀ n, m. dropn(n, lax0.to-adr(m)) = dropn(n, lax0).to-adr(m) ⊦ m2 + 1 = 0, dropn(m2, lax0.to-adr(m)) = (@(m0, m1) ' + lax0 = [] ⊃ [];dropn(m2 + 1 - 1, (@(m0, m1) ' + lax0).tail)).to-adr(m)

Rule argument

spec: list-prefixn, inst: laddress-list name: dropn-first seq: ⊦ n ≠ 0 → dropn(n, lax) = (lax = [] ⊃ [];dropn(n - 1, lax.tail)) subst: [lax, n] → [@(m0, m1) ' + lax0, m2 + 1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: @(m0, m1) ' + lax0, m2 + 1