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Proof step 49 from proof n2s-s2n-identity (previous step)

∀ m1. m1 < ((0 + 1) + 1) + 1 → true → s→n(n→s(m1)) = m1 ⊦ 2 = pos('3', '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ char ≠ char0 → pos(char, char0 ' + chars) = pos(char, chars) + 1
Proof step 51:
'3' ≠ '1', ∀ m1. m1 < ((0 + 1) + 1) + 1 → true → s→n(n→s(m1)) = m1 ⊦ 2 = pos('3', '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ') + 1

Rule argument

spec: list-del inst: charlist name: pos-n seq: ⊦ char ≠ char0 → pos(char, char0 ' + chars) = pos(char, chars) + 1 subst: [chars, char0, char] → [ '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ', '1', '3'] flags: rewrite

Additional information

Used terms: '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ', '1', '3'