Nuprl Lemma : eq_cons_imp_eq_tls
∀[A:Type]. ∀[a,b:A]. ∀[as,bs:A List]. as = bs ∈ (A List) supposing [a / as] = [b / bs] ∈ (A List)
Proof
Definitions occuring in Statement :
cons: [a / b],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
top: Top,
prop: ℙ,
uimplies: b supposing a
Lemmas referenced :
tl_wf,
reduce_tl_cons_lemma,
equal_wf,
list_wf,
cons_wf
Rules used in proof :
cut,
applyLambdaEquality,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
Error :universeIsType,
Error :inhabitedIsType,
because_Cache,
universeEquality,
Error :isect_memberFormation_alt,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[A:Type]. \mforall{}[a,b:A]. \mforall{}[as,bs:A List]. as = bs supposing [a / as] = [b / bs]
Date html generated:
2019_06_20-PM-00_38_59
Last ObjectModification:
2018_09_26-PM-02_07_29
Theory : list_0
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