Nuprl Lemma : test-change-equality
∀[L1:ℕ List]. ∀[L2:ℤ List]. ((L1 = L2 ∈ (ℤ List)) ⇒ (L1 = L2 ∈ (ℕ List)))
Proof
Definitions occuring in Statement :
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
list_subtype_base,
nat_wf,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
list_wf,
change-equality-type,
respects-equality-list,
subtype-base-respects-equality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
Error :equalityIstype,
because_Cache,
cut,
hypothesisEquality,
applyEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
sqequalRule,
intEquality,
Error :lambdaEquality_alt,
closedConclusion,
natural_numberEquality,
sqequalBase,
equalitySymmetry,
Error :universeIsType,
independent_functionElimination,
dependent_functionElimination,
equalityTransitivity
Latex:
\mforall{}[L1:\mBbbN{} List]. \mforall{}[L2:\mBbbZ{} List]. ((L1 = L2) {}\mRightarrow{} (L1 = L2))
Date html generated:
2019_06_20-PM-01_49_13
Last ObjectModification:
2018_11_29-PM-05_52_22
Theory : list_1
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