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Proof step 19 from proof n2s-s2n-identity (previous step)

m < 10, ∀ m1. m1 < m → true → s→n(n→s(m1)) = m1 ⊦ pos (('0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m], '0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ') = m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
n ≠ 0 ⊦ (char ' + chars)[(* n)] = chars[n -1]
Proof step 21:
m ≠ 0, m < 10, ∀ m1. m1 < m → true → s→n(n→s(m1)) = m1 ⊦ pos (('1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m -1], '0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ') = m

Rule argument

spec: list-del inst: charlist name: get-numrec seq: n ≠ 0 ⊦ (char ' + chars)[(* n)] = chars[n -1] subst: [n, chars, char] → [m, '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ', '0'] flags: rewrite

Additional information

Used simplifier rules: get-zero-01: ⊦ (char ' + chars)[0] = char; from specification list-del[charlist]%a: ⊦ (chars + chars0) + chars1 = chars + chars0 + chars1; from specification list[charlist]%pos-y: ⊦ pos(char, char ' + chars) = 0; from specification list-del[charlist] Used terms: m, '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ', '0'