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Proof step 4 from proof pos-range (previous step)

# str0 + 1 < pos(char, char0 ' + str0), ∀ char. # str0 < pos(char, str0) → pos(char, str0) = 0 ⊦ pos(char, char0 ' + str0) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ char1 ≠ char2 → pos(char1, char2 ' + str) = pos(char1, str) + 1
Proof step 6:
char ≠ char0, # str0 + 1 < pos(char, str0) + 1, ∀ char. # str0 < pos(char, str0) → pos(char, str0) = 0 ⊦ pos(char, str0) + 1 = 0

Rule argument

spec: string-less inst: name: Pos-rec seq: ⊦ char1 ≠ char2 → pos(char1, char2 ' + str) = pos(char1, str) + 1 subst: [str, char2, char1] → [str0, char0, char] flags: rewrite, current

Additional information

Used simplifier rules: Pos-found: ⊦ pos(char, char ' + str) = 0;%assoc: ⊦ (str1 + str2) + str3 = str1 + str2 + str3; from specification string-append Used terms: str0, char0, char