[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 94 from proof n2s-s2n-identity (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 95:
n ≠ 0 ⊦ (char ' + chars)[(* n)] = chars[n -1]
Proof step 96:
¬ m ≠ 0, m < 4, ∀ m1. m1 < (((((m + 1) + 1) + 1) + 1) + 1) + 1 → true → s→n(n→s(m1)) = m1 ⊦ pos(('6' ' + '7' ' + '8' ' + '9' ')[m], '0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ') = 6 + m
Proof step 114:
m ≠ 0, m < 4, ∀ m1. m1 < (((((m + 1) + 1) + 1) + 1) + 1) + 1 → true → s→n(n→s(m1)) = m1 ⊦ pos(('7' ' + '8' ' + '9' ')[m -1], '0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ') = 6 + 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, '7' ' + '8' ' + '9' ', '6'] flags: rewrite

Additional information

Used terms: m, '7' ' + '8' ' + '9' ', '6'