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Proof step 10 from proof lastn-restn-01 (previous step)

# y = n0 + n1, ∀ x, n0. # x = n0 + n1 → lastn(n1, x) = restn(n0, x) ⊦ lastn(n1, y) + a ' = restn(n0, y + a ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ n ≤ # x → restn(n, x + y) = restn(n, x) + y
Proof step 12:
# y = n0 + n1, n0 ≤ # y, ∀ x, n0. # x = n0 + n1 → lastn(n1, x) = restn(n0, x) ⊦ lastn(n1, y) + a ' = restn(n0, y) + a '

Rule argument

spec: <toplevel> name: restN-append seq: ⊦ n ≤ # x → restn(n, x + y) = restn(n, x) + y subst: [y, x, n] → [a ', y, n0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: a ', y, n0