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Proof step 11 from proof to-to-leq-inf (previous step)

n0 < #((nf to n0) + nf(n0) '), ∀ m, nf. m ≤ n0 → (nf to n0) to m = nf to m ⊦ ((nf to n0) + nf(n0) ' to n0) + ((nf to n0) + nf(n0) ')[n0] ' = nf to n0 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
∀ m, nf. m ≤ n0 → (nf to n0) to m = nf to m ⊦ ((nf to n0) + nf(n0) ' to n0) + ((nf to n0) + nf(n0) ')[n0] ' = nf to n0 + 1

Rule argument

Additional information

Used simplifier rules: size-inf-to: ⊦ #(nf to n) = n;%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%a: ⊦ (x + y) + z = x + y + z; from specification list%len-02: ⊦ # a ' = 0 +1; from specification list%len: ⊦ #(x + y) = # x + # y; from specification list