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Proof step 10 from proof to-to-leq-inf (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
m < # x ⊦ x to m + 1 = (x to m) + x[m] '
Proof step 12:
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

Rule argument

spec: <toplevel> name: to-unwind-end-fin seq: m < # x ⊦ x to m + 1 = (x to m) + x[m] ' subst: [m, x] → [n0, (nf to n0) + nf(n0) '] flags: <all paths>

Additional information

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