Nuprl Lemma : respects-equality-partial
∀[T:Type]. respects-equality(partial(T);T) supposing value-type(T)
Proof
Definitions occuring in Statement :
partial: partial(T),
value-type: value-type(T),
uimplies: b supposing a,
respects-equality: respects-equality(S;T),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
respects-equality: respects-equality(S;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
shorter-proof-of-termination-equality,
value-type-has-value,
partial_wf,
istype-base,
value-type_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
equalityTransitivity,
equalitySymmetry,
independent_pairFormation,
sqequalRule,
Error :equalityIstype,
Error :universeIsType,
because_Cache,
sqequalBase,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. respects-equality(partial(T);T) supposing value-type(T)
Date html generated:
2019_06_20-PM-00_33_57
Last ObjectModification:
2018_12_22-PM-01_16_36
Theory : partial_1
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