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Proof step 6 from proof inv-get-inverse-succ (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 7:
leninv(nσ) = ∞, ⌜n⌝ < leninv(nσ), ⌜⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ [n]⌝ + ⌜1⌝ < # nσ, stutf(nσ) ⊦ nσ [ (leninv(nσ) = ∞ ⊃ ⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ ;⌜(λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to leninv(nσ).n⌝ )[n] + 1 ] = n + 1
Proof step 56:
⌜n⌝ < leninv(nσ), ⌜⌜(λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to leninv(nσ).n⌝ [n]⌝ + ⌜1⌝ < # nσ, stutf(nσ) ⊦ nσ [ (leninv(nσ) = ∞ ⊃ ⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ ;⌜(λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to leninv(nσ).n⌝ )[n] + 1 ] = n + 1, leninv(nσ) = ∞

Rule argument

pos: left 2

Proof step 6 from proof inv-get-inverse-succ (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information