Nuprl Lemma : list_eq_imp_sqeq
∀T:Type. ∀L1,L2:T List. ((L1 = L2 ∈ (T List)) ⇒ (L1 ~ L2)) supposing T ⊆r Base
Proof
Definitions occuring in Statement :
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
base: Base,
universe: Type,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
sq_type: SQType(T),
guard: {T},
prop: ℙ
Lemmas referenced :
subtype_base_sq,
list_wf,
list_subtype_base,
equal_wf,
subtype_rel_wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesisEquality,
hypothesis,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
sqequalRule,
lambdaEquality,
sqequalAxiom,
because_Cache,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}L1,L2:T List. ((L1 = L2) {}\mRightarrow{} (L1 \msim{} L2)) supposing T \msubseteq{}r Base
Date html generated:
2017_04_17-AM-07_59_13
Last ObjectModification:
2017_02_27-PM-04_30_14
Theory : list_1
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