[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 6 from proof from-from (previous step)

n + m ≤ # x0 + 1, ∀ n, m. n + m ≤ # x0 → x0 from m from n = x0 from m + n ⊦ a ' + x0 from m from n = a ' + x0 from m + n

User applied rule structural induction

And obtained the following new goals

Proof step 7:
∀ n, x0, a. n + m0 ≤ # x0 + 1 ∧ (∀ n, m. n + m ≤ # x0 → x0 from m from n = x0 from m + n) → a ' + x0 from m0 from n = a ' + x0 from m0 + n, n + m0 +1 ≤ # x0 + 1, ∀ n, m. n + m ≤ # x0 → x0 from m from n = x0 from m + n ⊦ a ' + x0 from m0 +1 from n = a ' + x0 from m0 +1 + n

Rule argument

indvar: m

Additional information

Used simplifier rules: from-zero-l: ⊦ x from 0 = x;%nat freely generated by 0, +1;;%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2