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Proof step 9 from proof inv-get-inverse-succ (previous step)

stutf(nσ), # nσ = ∞, ⌜n⌝ < leninv(nσ), stutf(nσ), ∀ m. ∃ m0. m < nσ[m0], ∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0] ⊦ nσ [ (# nσ = ∞ ∧ (∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0]) ⊃ ⌜λ m. max∞(λ n0. nσ[n0] = m).n⌝ ;⌜(λ m. max∞(λ n0. nσ[n0] = m).n) to leninv(nσ).n⌝ ) [n ] + 1 ] = n + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# nσ = ∞, ⌜n⌝ < leninv(nσ), stutf(nσ), ∀ m. ∃ m0. m < nσ[m0], ∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0] ⊦ nσ[max∞(λ n0. nσ[n0] = n).n + 1] = n + 1

Rule argument

Additional information

Used simplifier rules: sel-inf: ⊦ ⌜nnf⌝ [n] = nnf(n); from specification stream[natstream]