Nuprl Lemma : absolutelyfree-unique
∀[T,S:Type]. (absolutelyfree{i:l}(T) ⇒ absolutelyfree{i:l}(S) ⇒ T ≡ S)
Proof
Definitions occuring in Statement :
absolutelyfree: absolutelyfree{i:l}(T),
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
absolutelyfree: absolutelyfree{i:l}(T),
and: P ∧ Q,
ext-eq: A ≡ B,
all: ∀x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
absolutelyfree_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
hypothesis,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
extract_by_obid,
isectElimination,
cumulativity,
sqequalRule,
lambdaEquality,
independent_pairEquality,
axiomEquality,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T,S:Type]. (absolutelyfree\{i:l\}(T) {}\mRightarrow{} absolutelyfree\{i:l\}(S) {}\mRightarrow{} T \mequiv{} S)
Date html generated:
2017_09_29-PM-06_10_45
Last ObjectModification:
2017_04_21-PM-00_38_20
Theory : continuity
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